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Question 1 of 190
Bill Gates attended a English Spelling Bee Competition. Bill Gates answered all 116 questions. For each correct answer, Bill Gates will get 10 marks. However, for each wrong answer, Bill Gates will be deducted by 2 mark(s). If Bill Gates scored 200 marks in total, how many questions did Bill Gates answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Bill Gates answered all the 116 questions correctly, and each correct answer has 10 marks, then Bill Gates should score 1160 marks,
\begin{array}{rcl}
116\times10=1160.
\end{array}
For every question Bill Gates answered wrongly, Bill Gates will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Bill Gates only scored 200 marks, therefore Bill Gates totally lost
\begin{array}{rcl}
1160-200=960.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
960\div12=80.
\end{array}
The number of correct answers is
\begin{array}{rcl}
116-80=36.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 116, we have,
\begin{array}{rcl}
C+W=116.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=200.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=232.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=432.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&432\div12\\
&=&36.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&116-36\\
&=&80.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Bill Gates answered all the 116 questions correctly, and each correct answer has 10 marks, then Bill Gates should score 1160 marks,
\begin{array}{rcl}
116\times10=1160.
\end{array}
For every question Bill Gates answered wrongly, Bill Gates will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Bill Gates only scored 200 marks, therefore Bill Gates totally lost
\begin{array}{rcl}
1160-200=960.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
960\div12=80.
\end{array}
The number of correct answers is
\begin{array}{rcl}
116-80=36.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 116, we have,
\begin{array}{rcl}
C+W=116.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=200.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=232.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=432.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&432\div12\\
&=&36.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&116-36\\
&=&80.\tag{6}
\end{array}
Noah attended a South-East Asia Maths Olympaid (SEAMO). Noah answered all 92 questions. For each correct answer, Noah will get 6 marks. However, for each wrong answer, Noah will be deducted by 2 mark(s). If Noah scored 72 marks in total, how many questions did Noah answer correctly?
Sorry. Please check the correct answer below.
You are Right
Method 1: Method of Assumption
Assume Noah answered all the 92 questions correctly, and each correct answer has 6 marks, then Noah should score 552 marks,
\begin{array}{rcl}
92\times6=552.
\end{array}
For every question Noah answered wrongly, Noah will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Noah only scored 72 marks, therefore Noah totally lost
\begin{array}{rcl}
552-72=480.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
480\div8=60.
\end{array}
The number of correct answers is
\begin{array}{rcl}
92-60=32.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 92, we have,
\begin{array}{rcl}
C+W=92.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=72.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=184.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=256.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&256\div8\\
&=&32.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&92-32\\
&=&60.\tag{6}
\end{array}
Noah attended a Maths Competition. Noah answered all 72 questions. For each correct answer, Noah will get 4 marks. However, for each wrong answer, Noah will be deducted by 2 mark(s). If Noah scored 48 marks in total, how many questions did Noah answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Noah answered all the 72 questions correctly, and each correct answer has 4 marks, then Noah should score 288 marks,
\begin{array}{rcl}
72\times4=288.
\end{array}
For every question Noah answered wrongly, Noah will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Noah only scored 48 marks, therefore Noah totally lost
\begin{array}{rcl}
288-48=240.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
240\div6=40.
\end{array}
The number of correct answers is
\begin{array}{rcl}
72-40=32.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 72, we have,
\begin{array}{rcl}
C+W=72.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=48.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=144.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=192.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&192\div6\\
&=&32.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&72-32\\
&=&40.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Noah answered all the 72 questions correctly, and each correct answer has 4 marks, then Noah should score 288 marks,
\begin{array}{rcl}
72\times4=288.
\end{array}
For every question Noah answered wrongly, Noah will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Noah only scored 48 marks, therefore Noah totally lost
\begin{array}{rcl}
288-48=240.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
240\div6=40.
\end{array}
The number of correct answers is
\begin{array}{rcl}
72-40=32.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 72, we have,
\begin{array}{rcl}
C+W=72.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=48.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=144.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=192.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&192\div6\\
&=&32.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&72-32\\
&=&40.\tag{6}
\end{array}
Sophia attended a Maths Competition. Sophia answered all 73 questions. For each correct answer, Sophia will get 5 marks. However, for each wrong answer, Sophia will be deducted by 1 mark(s). If Sophia scored 95 marks in total, how many questions did Sophia answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Sophia answered all the 73 questions correctly, and each correct answer has 5 marks, then Sophia should score 365 marks,
\begin{array}{rcl}
73\times5=365.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Sophia only scored 95 marks, therefore Sophia totally lost
\begin{array}{rcl}
365-95=270.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
270\div6=45.
\end{array}
The number of correct answers is
\begin{array}{rcl}
73-45=28.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 73, we have,
\begin{array}{rcl}
C+W=73.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=95.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=168.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&168\div6\\
&=&28.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&73-28\\
&=&45.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Sophia answered all the 73 questions correctly, and each correct answer has 5 marks, then Sophia should score 365 marks,
\begin{array}{rcl}
73\times5=365.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Sophia only scored 95 marks, therefore Sophia totally lost
\begin{array}{rcl}
365-95=270.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
270\div6=45.
\end{array}
The number of correct answers is
\begin{array}{rcl}
73-45=28.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 73, we have,
\begin{array}{rcl}
C+W=73.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=95.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=168.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&168\div6\\
&=&28.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&73-28\\
&=&45.\tag{6}
\end{array}
James attended a English Spelling Bee Competition. James answered all 25 questions. For each correct answer, James will get 3 marks. However, for each wrong answer, James will be deducted by 1 mark(s). If James scored 39 marks in total, how many questions did James answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume James answered all the 25 questions correctly, and each correct answer has 3 marks, then James should score 75 marks,
\begin{array}{rcl}
25\times3=75.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since James only scored 39 marks, therefore James totally lost
\begin{array}{rcl}
75-39=36.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
36\div4=9.
\end{array}
The number of correct answers is
\begin{array}{rcl}
25-9=16.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 25, we have,
\begin{array}{rcl}
C+W=25.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=39.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=64.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&64\div4\\
&=&16.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&25-16\\
&=&9.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume James answered all the 25 questions correctly, and each correct answer has 3 marks, then James should score 75 marks,
\begin{array}{rcl}
25\times3=75.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since James only scored 39 marks, therefore James totally lost
\begin{array}{rcl}
75-39=36.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
36\div4=9.
\end{array}
The number of correct answers is
\begin{array}{rcl}
25-9=16.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 25, we have,
\begin{array}{rcl}
C+W=25.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=39.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=64.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&64\div4\\
&=&16.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&25-16\\
&=&9.\tag{6}
\end{array}
James attended a Chinese Multiple Choices Test. James answered all 66 questions. For each correct answer, James will get 5 marks. However, for each wrong answer, James will be deducted by 1 mark(s). If James scored 60 marks in total, how many questions did James answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume James answered all the 66 questions correctly, and each correct answer has 5 marks, then James should score 330 marks,
\begin{array}{rcl}
66\times5=330.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since James only scored 60 marks, therefore James totally lost
\begin{array}{rcl}
330-60=270.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
270\div6=45.
\end{array}
The number of correct answers is
\begin{array}{rcl}
66-45=21.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 66, we have,
\begin{array}{rcl}
C+W=66.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=60.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=126.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&126\div6\\
&=&21.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&66-21\\
&=&45.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume James answered all the 66 questions correctly, and each correct answer has 5 marks, then James should score 330 marks,
\begin{array}{rcl}
66\times5=330.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since James only scored 60 marks, therefore James totally lost
\begin{array}{rcl}
330-60=270.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
270\div6=45.
\end{array}
The number of correct answers is
\begin{array}{rcl}
66-45=21.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 66, we have,
\begin{array}{rcl}
C+W=66.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=60.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=126.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&126\div6\\
&=&21.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&66-21\\
&=&45.\tag{6}
\end{array}
Larry Page attended a Singapore Maths Olympaid (SMO). Larry Page answered all 29 questions. For each correct answer, Larry Page will get 2 marks. However, for each wrong answer, Larry Page will be deducted by 1 mark(s). If Larry Page scored 40 marks in total, how many questions did Larry Page answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Larry Page answered all the 29 questions correctly, and each correct answer has 2 marks, then Larry Page should score 58 marks,
\begin{array}{rcl}
29\times2=58.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Larry Page only scored 40 marks, therefore Larry Page totally lost
\begin{array}{rcl}
58-40=18.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
18\div3=6.
\end{array}
The number of correct answers is
\begin{array}{rcl}
29-6=23.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 29, we have,
\begin{array}{rcl}
C+W=29.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=40.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=69.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&69\div3\\
&=&23.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&29-23\\
&=&6.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Larry Page answered all the 29 questions correctly, and each correct answer has 2 marks, then Larry Page should score 58 marks,
\begin{array}{rcl}
29\times2=58.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Larry Page only scored 40 marks, therefore Larry Page totally lost
\begin{array}{rcl}
58-40=18.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
18\div3=6.
\end{array}
The number of correct answers is
\begin{array}{rcl}
29-6=23.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 29, we have,
\begin{array}{rcl}
C+W=29.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=40.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=69.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&69\div3\\
&=&23.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&29-23\\
&=&6.\tag{6}
\end{array}
James attended a Australian Maths Trust (AMT). James answered all 49 questions. For each correct answer, James will get 4 marks. However, for each wrong answer, James will be deducted by 1 mark(s). If James scored 56 marks in total, how many questions did James answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume James answered all the 49 questions correctly, and each correct answer has 4 marks, then James should score 196 marks,
\begin{array}{rcl}
49\times4=196.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since James only scored 56 marks, therefore James totally lost
\begin{array}{rcl}
196-56=140.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
140\div5=28.
\end{array}
The number of correct answers is
\begin{array}{rcl}
49-28=21.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 49, we have,
\begin{array}{rcl}
C+W=49.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=56.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=105.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&105\div5\\
&=&21.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&49-21\\
&=&28.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume James answered all the 49 questions correctly, and each correct answer has 4 marks, then James should score 196 marks,
\begin{array}{rcl}
49\times4=196.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since James only scored 56 marks, therefore James totally lost
\begin{array}{rcl}
196-56=140.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
140\div5=28.
\end{array}
The number of correct answers is
\begin{array}{rcl}
49-28=21.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 49, we have,
\begin{array}{rcl}
C+W=49.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=56.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=105.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&105\div5\\
&=&21.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&49-21\\
&=&28.\tag{6}
\end{array}
Emma attended a English Spelling Bee Competition. Emma answered all 45 questions. For each correct answer, Emma will get 4 marks. However, for each wrong answer, Emma will be deducted by 1 mark(s). If Emma scored 80 marks in total, how many questions did Emma answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Emma answered all the 45 questions correctly, and each correct answer has 4 marks, then Emma should score 180 marks,
\begin{array}{rcl}
45\times4=180.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Emma only scored 80 marks, therefore Emma totally lost
\begin{array}{rcl}
180-80=100.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
100\div5=20.
\end{array}
The number of correct answers is
\begin{array}{rcl}
45-20=25.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 45, we have,
\begin{array}{rcl}
C+W=45.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=80.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=125.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&125\div5\\
&=&25.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&45-25\\
&=&20.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Emma answered all the 45 questions correctly, and each correct answer has 4 marks, then Emma should score 180 marks,
\begin{array}{rcl}
45\times4=180.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Emma only scored 80 marks, therefore Emma totally lost
\begin{array}{rcl}
180-80=100.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
100\div5=20.
\end{array}
The number of correct answers is
\begin{array}{rcl}
45-20=25.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 45, we have,
\begin{array}{rcl}
C+W=45.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=80.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=125.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&125\div5\\
&=&25.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&45-25\\
&=&20.\tag{6}
\end{array}
Larry Page attended a Maths Competition. Larry Page answered all 31 questions. For each correct answer, Larry Page will get 2 marks. However, for each wrong answer, Larry Page will be deducted by 1 mark(s). If Larry Page scored 26 marks in total, how many questions did Larry Page answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Larry Page answered all the 31 questions correctly, and each correct answer has 2 marks, then Larry Page should score 62 marks,
\begin{array}{rcl}
31\times2=62.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Larry Page only scored 26 marks, therefore Larry Page totally lost
\begin{array}{rcl}
62-26=36.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
36\div3=12.
\end{array}
The number of correct answers is
\begin{array}{rcl}
31-12=19.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 31, we have,
\begin{array}{rcl}
C+W=31.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=26.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=57.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&57\div3\\
&=&19.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&31-19\\
&=&12.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Larry Page answered all the 31 questions correctly, and each correct answer has 2 marks, then Larry Page should score 62 marks,
\begin{array}{rcl}
31\times2=62.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Larry Page only scored 26 marks, therefore Larry Page totally lost
\begin{array}{rcl}
62-26=36.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
36\div3=12.
\end{array}
The number of correct answers is
\begin{array}{rcl}
31-12=19.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 31, we have,
\begin{array}{rcl}
C+W=31.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=26.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=57.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&57\div3\\
&=&19.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&31-19\\
&=&12.\tag{6}
\end{array}
Benjamin attended a Maths Competition. Benjamin answered all 35 questions. For each correct answer, Benjamin will get 8 marks. However, for each wrong answer, Benjamin will be deducted by 2 mark(s). If Benjamin scored 120 marks in total, how many questions did Benjamin answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Benjamin answered all the 35 questions correctly, and each correct answer has 8 marks, then Benjamin should score 280 marks,
\begin{array}{rcl}
35\times8=280.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Benjamin only scored 120 marks, therefore Benjamin totally lost
\begin{array}{rcl}
280-120=160.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
160\div10=16.
\end{array}
The number of correct answers is
\begin{array}{rcl}
35-16=19.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 35, we have,
\begin{array}{rcl}
C+W=35.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=120.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=70.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=190.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&190\div10\\
&=&19.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&35-19\\
&=&16.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Benjamin answered all the 35 questions correctly, and each correct answer has 8 marks, then Benjamin should score 280 marks,
\begin{array}{rcl}
35\times8=280.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Benjamin only scored 120 marks, therefore Benjamin totally lost
\begin{array}{rcl}
280-120=160.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
160\div10=16.
\end{array}
The number of correct answers is
\begin{array}{rcl}
35-16=19.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 35, we have,
\begin{array}{rcl}
C+W=35.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=120.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=70.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=190.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&190\div10\\
&=&19.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&35-19\\
&=&16.\tag{6}
\end{array}
Emma attended a South-East Asia Maths Olympaid (SEAMO). Emma answered all 43 questions. For each correct answer, Emma will get 3 marks. However, for each wrong answer, Emma will be deducted by 1 mark(s). If Emma scored 33 marks in total, how many questions did Emma answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Emma answered all the 43 questions correctly, and each correct answer has 3 marks, then Emma should score 129 marks,
\begin{array}{rcl}
43\times3=129.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Emma only scored 33 marks, therefore Emma totally lost
\begin{array}{rcl}
129-33=96.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
96\div4=24.
\end{array}
The number of correct answers is
\begin{array}{rcl}
43-24=19.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 43, we have,
\begin{array}{rcl}
C+W=43.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=33.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=76.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&76\div4\\
&=&19.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&43-19\\
&=&24.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Emma answered all the 43 questions correctly, and each correct answer has 3 marks, then Emma should score 129 marks,
\begin{array}{rcl}
43\times3=129.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Emma only scored 33 marks, therefore Emma totally lost
\begin{array}{rcl}
129-33=96.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
96\div4=24.
\end{array}
The number of correct answers is
\begin{array}{rcl}
43-24=19.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 43, we have,
\begin{array}{rcl}
C+W=43.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=33.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=76.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&76\div4\\
&=&19.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&43-19\\
&=&24.\tag{6}
\end{array}
Jacob attended a Maths Competition. Jacob answered all 108 questions. For each correct answer, Jacob will get 8 marks. However, for each wrong answer, Jacob will be deducted by 2 mark(s). If Jacob scored 144 marks in total, how many questions did Jacob answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Jacob answered all the 108 questions correctly, and each correct answer has 8 marks, then Jacob should score 864 marks,
\begin{array}{rcl}
108\times8=864.
\end{array}
For every question Jacob answered wrongly, Jacob will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Jacob only scored 144 marks, therefore Jacob totally lost
\begin{array}{rcl}
864-144=720.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
720\div10=72.
\end{array}
The number of correct answers is
\begin{array}{rcl}
108-72=36.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 108, we have,
\begin{array}{rcl}
C+W=108.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=144.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=216.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=360.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&360\div10\\
&=&36.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&108-36\\
&=&72.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Jacob answered all the 108 questions correctly, and each correct answer has 8 marks, then Jacob should score 864 marks,
\begin{array}{rcl}
108\times8=864.
\end{array}
For every question Jacob answered wrongly, Jacob will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Jacob only scored 144 marks, therefore Jacob totally lost
\begin{array}{rcl}
864-144=720.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
720\div10=72.
\end{array}
The number of correct answers is
\begin{array}{rcl}
108-72=36.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 108, we have,
\begin{array}{rcl}
C+W=108.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=144.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=216.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=360.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&360\div10\\
&=&36.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&108-36\\
&=&72.\tag{6}
\end{array}
Larry Page attended a English Spelling Bee Competition. Larry Page answered all 67 questions. For each correct answer, Larry Page will get 4 marks. However, for each wrong answer, Larry Page will be deducted by 2 mark(s). If Larry Page scored 52 marks in total, how many questions did Larry Page answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Larry Page answered all the 67 questions correctly, and each correct answer has 4 marks, then Larry Page should score 268 marks,
\begin{array}{rcl}
67\times4=268.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Larry Page only scored 52 marks, therefore Larry Page totally lost
\begin{array}{rcl}
268-52=216.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
216\div6=36.
\end{array}
The number of correct answers is
\begin{array}{rcl}
67-36=31.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 67, we have,
\begin{array}{rcl}
C+W=67.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=52.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=134.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=186.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&186\div6\\
&=&31.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&67-31\\
&=&36.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Larry Page answered all the 67 questions correctly, and each correct answer has 4 marks, then Larry Page should score 268 marks,
\begin{array}{rcl}
67\times4=268.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Larry Page only scored 52 marks, therefore Larry Page totally lost
\begin{array}{rcl}
268-52=216.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
216\div6=36.
\end{array}
The number of correct answers is
\begin{array}{rcl}
67-36=31.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 67, we have,
\begin{array}{rcl}
C+W=67.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=52.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=134.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=186.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&186\div6\\
&=&31.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&67-31\\
&=&36.\tag{6}
\end{array}
Olivia attended a American Maths Olympiad (AMO). Olivia answered all 43 questions. For each correct answer, Olivia will get 2 marks. However, for each wrong answer, Olivia will be deducted by 1 mark(s). If Olivia scored 32 marks in total, how many questions did Olivia answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Olivia answered all the 43 questions correctly, and each correct answer has 2 marks, then Olivia should score 86 marks,
\begin{array}{rcl}
43\times2=86.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Olivia only scored 32 marks, therefore Olivia totally lost
\begin{array}{rcl}
86-32=54.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
54\div3=18.
\end{array}
The number of correct answers is
\begin{array}{rcl}
43-18=25.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 43, we have,
\begin{array}{rcl}
C+W=43.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=32.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=75.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&75\div3\\
&=&25.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&43-25\\
&=&18.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Olivia answered all the 43 questions correctly, and each correct answer has 2 marks, then Olivia should score 86 marks,
\begin{array}{rcl}
43\times2=86.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Olivia only scored 32 marks, therefore Olivia totally lost
\begin{array}{rcl}
86-32=54.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
54\div3=18.
\end{array}
The number of correct answers is
\begin{array}{rcl}
43-18=25.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 43, we have,
\begin{array}{rcl}
C+W=43.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=32.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=75.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&75\div3\\
&=&25.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&43-25\\
&=&18.\tag{6}
\end{array}
Benjamin attended a Singapore Maths Olympaid (SMO). Benjamin answered all 50 questions. For each correct answer, Benjamin will get 10 marks. However, for each wrong answer, Benjamin will be deducted by 2 mark(s). If Benjamin scored 140 marks in total, how many questions did Benjamin answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Benjamin answered all the 50 questions correctly, and each correct answer has 10 marks, then Benjamin should score 500 marks,
\begin{array}{rcl}
50\times10=500.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Benjamin only scored 140 marks, therefore Benjamin totally lost
\begin{array}{rcl}
500-140=360.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
360\div12=30.
\end{array}
The number of correct answers is
\begin{array}{rcl}
50-30=20.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 50, we have,
\begin{array}{rcl}
C+W=50.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=140.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=100.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=240.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&240\div12\\
&=&20.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&50-20\\
&=&30.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Benjamin answered all the 50 questions correctly, and each correct answer has 10 marks, then Benjamin should score 500 marks,
\begin{array}{rcl}
50\times10=500.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Benjamin only scored 140 marks, therefore Benjamin totally lost
\begin{array}{rcl}
500-140=360.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
360\div12=30.
\end{array}
The number of correct answers is
\begin{array}{rcl}
50-30=20.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 50, we have,
\begin{array}{rcl}
C+W=50.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=140.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=100.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=240.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&240\div12\\
&=&20.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&50-20\\
&=&30.\tag{6}
\end{array}
Sophia attended a Chinese Multiple Choices Test. Sophia answered all 87 questions. For each correct answer, Sophia will get 6 marks. However, for each wrong answer, Sophia will be deducted by 2 mark(s). If Sophia scored 90 marks in total, how many questions did Sophia answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Sophia answered all the 87 questions correctly, and each correct answer has 6 marks, then Sophia should score 522 marks,
\begin{array}{rcl}
87\times6=522.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Sophia only scored 90 marks, therefore Sophia totally lost
\begin{array}{rcl}
522-90=432.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
432\div8=54.
\end{array}
The number of correct answers is
\begin{array}{rcl}
87-54=33.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 87, we have,
\begin{array}{rcl}
C+W=87.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=90.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=174.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=264.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&264\div8\\
&=&33.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&87-33\\
&=&54.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Sophia answered all the 87 questions correctly, and each correct answer has 6 marks, then Sophia should score 522 marks,
\begin{array}{rcl}
87\times6=522.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Sophia only scored 90 marks, therefore Sophia totally lost
\begin{array}{rcl}
522-90=432.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
432\div8=54.
\end{array}
The number of correct answers is
\begin{array}{rcl}
87-54=33.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 87, we have,
\begin{array}{rcl}
C+W=87.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=90.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=174.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=264.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&264\div8\\
&=&33.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&87-33\\
&=&54.\tag{6}
\end{array}
Sophia attended a American Maths Olympiad (AMO). Sophia answered all 24 questions. For each correct answer, Sophia will get 4 marks. However, for each wrong answer, Sophia will be deducted by 2 mark(s). If Sophia scored 48 marks in total, how many questions did Sophia answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Sophia answered all the 24 questions correctly, and each correct answer has 4 marks, then Sophia should score 96 marks,
\begin{array}{rcl}
24\times4=96.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Sophia only scored 48 marks, therefore Sophia totally lost
\begin{array}{rcl}
96-48=48.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
48\div6=8.
\end{array}
The number of correct answers is
\begin{array}{rcl}
24-8=16.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 24, we have,
\begin{array}{rcl}
C+W=24.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=48.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=48.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=96.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&96\div6\\
&=&16.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&24-16\\
&=&8.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Sophia answered all the 24 questions correctly, and each correct answer has 4 marks, then Sophia should score 96 marks,
\begin{array}{rcl}
24\times4=96.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Sophia only scored 48 marks, therefore Sophia totally lost
\begin{array}{rcl}
96-48=48.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
48\div6=8.
\end{array}
The number of correct answers is
\begin{array}{rcl}
24-8=16.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 24, we have,
\begin{array}{rcl}
C+W=24.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=48.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=48.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=96.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&96\div6\\
&=&16.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&24-16\\
&=&8.\tag{6}
\end{array}
William attended a Maths Competition. William answered all 10 questions. For each correct answer, William will get 2 marks. However, for each wrong answer, William will be deducted by 1 mark(s). If William scored 20 marks in total, how many questions did William answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume William answered all the 10 questions correctly, and each correct answer has 2 marks, then William should score 20 marks,
\begin{array}{rcl}
10\times2=20.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since William only scored 20 marks, therefore William totally lost
\begin{array}{rcl}
20-20=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div3=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
10-0=10.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 10, we have,
\begin{array}{rcl}
C+W=10.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=20.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=30.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&30\div3\\
&=&10.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&10-10\\
&=&0.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume William answered all the 10 questions correctly, and each correct answer has 2 marks, then William should score 20 marks,
\begin{array}{rcl}
10\times2=20.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since William only scored 20 marks, therefore William totally lost
\begin{array}{rcl}
20-20=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div3=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
10-0=10.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 10, we have,
\begin{array}{rcl}
C+W=10.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=20.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=30.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&30\div3\\
&=&10.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&10-10\\
&=&0.\tag{6}
\end{array}
Isabella attended a Chinese Multiple Choices Test. Isabella answered all 23 questions. For each correct answer, Isabella will get 3 marks. However, for each wrong answer, Isabella will be deducted by 1 mark(s). If Isabella scored 33 marks in total, how many questions did Isabella answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Isabella answered all the 23 questions correctly, and each correct answer has 3 marks, then Isabella should score 69 marks,
\begin{array}{rcl}
23\times3=69.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Isabella only scored 33 marks, therefore Isabella totally lost
\begin{array}{rcl}
69-33=36.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
36\div4=9.
\end{array}
The number of correct answers is
\begin{array}{rcl}
23-9=14.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 23, we have,
\begin{array}{rcl}
C+W=23.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=33.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=56.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&56\div4\\
&=&14.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&23-14\\
&=&9.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Isabella answered all the 23 questions correctly, and each correct answer has 3 marks, then Isabella should score 69 marks,
\begin{array}{rcl}
23\times3=69.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Isabella only scored 33 marks, therefore Isabella totally lost
\begin{array}{rcl}
69-33=36.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
36\div4=9.
\end{array}
The number of correct answers is
\begin{array}{rcl}
23-9=14.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 23, we have,
\begin{array}{rcl}
C+W=23.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=33.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=56.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&56\div4\\
&=&14.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&23-14\\
&=&9.\tag{6}
\end{array}
James attended a Australian Maths Trust (AMT). James answered all 23 questions. For each correct answer, James will get 3 marks. However, for each wrong answer, James will be deducted by 1 mark(s). If James scored 45 marks in total, how many questions did James answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume James answered all the 23 questions correctly, and each correct answer has 3 marks, then James should score 69 marks,
\begin{array}{rcl}
23\times3=69.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since James only scored 45 marks, therefore James totally lost
\begin{array}{rcl}
69-45=24.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
24\div4=6.
\end{array}
The number of correct answers is
\begin{array}{rcl}
23-6=17.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 23, we have,
\begin{array}{rcl}
C+W=23.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=45.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=68.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&68\div4\\
&=&17.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&23-17\\
&=&6.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume James answered all the 23 questions correctly, and each correct answer has 3 marks, then James should score 69 marks,
\begin{array}{rcl}
23\times3=69.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since James only scored 45 marks, therefore James totally lost
\begin{array}{rcl}
69-45=24.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
24\div4=6.
\end{array}
The number of correct answers is
\begin{array}{rcl}
23-6=17.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 23, we have,
\begin{array}{rcl}
C+W=23.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=45.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=68.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&68\div4\\
&=&17.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&23-17\\
&=&6.\tag{6}
\end{array}
Liam attended a Australian Maths Trust (AMT). Liam answered all 50 questions. For each correct answer, Liam will get 4 marks. However, for each wrong answer, Liam will be deducted by 1 mark(s). If Liam scored 60 marks in total, how many questions did Liam answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Liam answered all the 50 questions correctly, and each correct answer has 4 marks, then Liam should score 200 marks,
\begin{array}{rcl}
50\times4=200.
\end{array}
For every question Liam answered wrongly, Liam will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Liam only scored 60 marks, therefore Liam totally lost
\begin{array}{rcl}
200-60=140.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
140\div5=28.
\end{array}
The number of correct answers is
\begin{array}{rcl}
50-28=22.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 50, we have,
\begin{array}{rcl}
C+W=50.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=60.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=110.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&110\div5\\
&=&22.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&50-22\\
&=&28.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Liam answered all the 50 questions correctly, and each correct answer has 4 marks, then Liam should score 200 marks,
\begin{array}{rcl}
50\times4=200.
\end{array}
For every question Liam answered wrongly, Liam will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Liam only scored 60 marks, therefore Liam totally lost
\begin{array}{rcl}
200-60=140.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
140\div5=28.
\end{array}
The number of correct answers is
\begin{array}{rcl}
50-28=22.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 50, we have,
\begin{array}{rcl}
C+W=50.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=60.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=110.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&110\div5\\
&=&22.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&50-22\\
&=&28.\tag{6}
\end{array}
Liam attended a Singapore Maths Olympaid (SMO). Liam answered all 30 questions. For each correct answer, Liam will get 5 marks. However, for each wrong answer, Liam will be deducted by 1 mark(s). If Liam scored 90 marks in total, how many questions did Liam answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Liam answered all the 30 questions correctly, and each correct answer has 5 marks, then Liam should score 150 marks,
\begin{array}{rcl}
30\times5=150.
\end{array}
For every question Liam answered wrongly, Liam will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Liam only scored 90 marks, therefore Liam totally lost
\begin{array}{rcl}
150-90=60.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
60\div6=10.
\end{array}
The number of correct answers is
\begin{array}{rcl}
30-10=20.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 30, we have,
\begin{array}{rcl}
C+W=30.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=90.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=120.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&120\div6\\
&=&20.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&30-20\\
&=&10.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Liam answered all the 30 questions correctly, and each correct answer has 5 marks, then Liam should score 150 marks,
\begin{array}{rcl}
30\times5=150.
\end{array}
For every question Liam answered wrongly, Liam will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Liam only scored 90 marks, therefore Liam totally lost
\begin{array}{rcl}
150-90=60.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
60\div6=10.
\end{array}
The number of correct answers is
\begin{array}{rcl}
30-10=20.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 30, we have,
\begin{array}{rcl}
C+W=30.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=90.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=120.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&120\div6\\
&=&20.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&30-20\\
&=&10.\tag{6}
\end{array}
Sophia attended a South-East Asia Maths Olympaid (SEAMO). Sophia answered all 95 questions. For each correct answer, Sophia will get 6 marks. However, for each wrong answer, Sophia will be deducted by 2 mark(s). If Sophia scored 90 marks in total, how many questions did Sophia answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Sophia answered all the 95 questions correctly, and each correct answer has 6 marks, then Sophia should score 570 marks,
\begin{array}{rcl}
95\times6=570.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Sophia only scored 90 marks, therefore Sophia totally lost
\begin{array}{rcl}
570-90=480.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
480\div8=60.
\end{array}
The number of correct answers is
\begin{array}{rcl}
95-60=35.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 95, we have,
\begin{array}{rcl}
C+W=95.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=90.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=190.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=280.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&280\div8\\
&=&35.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&95-35\\
&=&60.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Sophia answered all the 95 questions correctly, and each correct answer has 6 marks, then Sophia should score 570 marks,
\begin{array}{rcl}
95\times6=570.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Sophia only scored 90 marks, therefore Sophia totally lost
\begin{array}{rcl}
570-90=480.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
480\div8=60.
\end{array}
The number of correct answers is
\begin{array}{rcl}
95-60=35.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 95, we have,
\begin{array}{rcl}
C+W=95.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=90.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=190.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=280.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&280\div8\\
&=&35.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&95-35\\
&=&60.\tag{6}
\end{array}
Larry Page attended a South-East Asia Maths Olympaid (SEAMO). Larry Page answered all 16 questions. For each correct answer, Larry Page will get 8 marks. However, for each wrong answer, Larry Page will be deducted by 2 mark(s). If Larry Page scored 128 marks in total, how many questions did Larry Page answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Larry Page answered all the 16 questions correctly, and each correct answer has 8 marks, then Larry Page should score 128 marks,
\begin{array}{rcl}
16\times8=128.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Larry Page only scored 128 marks, therefore Larry Page totally lost
\begin{array}{rcl}
128-128=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div10=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
16-0=16.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 16, we have,
\begin{array}{rcl}
C+W=16.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=128.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=32.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=160.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&160\div10\\
&=&16.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&16-16\\
&=&0.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Larry Page answered all the 16 questions correctly, and each correct answer has 8 marks, then Larry Page should score 128 marks,
\begin{array}{rcl}
16\times8=128.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Larry Page only scored 128 marks, therefore Larry Page totally lost
\begin{array}{rcl}
128-128=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div10=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
16-0=16.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 16, we have,
\begin{array}{rcl}
C+W=16.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=128.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=32.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=160.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&160\div10\\
&=&16.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&16-16\\
&=&0.\tag{6}
\end{array}
Emma attended a Singapore Maths Olympaid (SMO). Emma answered all 115 questions. For each correct answer, Emma will get 8 marks. However, for each wrong answer, Emma will be deducted by 2 mark(s). If Emma scored 120 marks in total, how many questions did Emma answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Emma answered all the 115 questions correctly, and each correct answer has 8 marks, then Emma should score 920 marks,
\begin{array}{rcl}
115\times8=920.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Emma only scored 120 marks, therefore Emma totally lost
\begin{array}{rcl}
920-120=800.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
800\div10=80.
\end{array}
The number of correct answers is
\begin{array}{rcl}
115-80=35.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 115, we have,
\begin{array}{rcl}
C+W=115.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=120.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=230.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=350.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&350\div10\\
&=&35.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&115-35\\
&=&80.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Emma answered all the 115 questions correctly, and each correct answer has 8 marks, then Emma should score 920 marks,
\begin{array}{rcl}
115\times8=920.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Emma only scored 120 marks, therefore Emma totally lost
\begin{array}{rcl}
920-120=800.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
800\div10=80.
\end{array}
The number of correct answers is
\begin{array}{rcl}
115-80=35.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 115, we have,
\begin{array}{rcl}
C+W=115.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=120.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=230.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=350.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&350\div10\\
&=&35.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&115-35\\
&=&80.\tag{6}
\end{array}
William attended a English Spelling Bee Competition. William answered all 38 questions. For each correct answer, William will get 2 marks. However, for each wrong answer, William will be deducted by 1 mark(s). If William scored 34 marks in total, how many questions did William answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume William answered all the 38 questions correctly, and each correct answer has 2 marks, then William should score 76 marks,
\begin{array}{rcl}
38\times2=76.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since William only scored 34 marks, therefore William totally lost
\begin{array}{rcl}
76-34=42.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
42\div3=14.
\end{array}
The number of correct answers is
\begin{array}{rcl}
38-14=24.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 38, we have,
\begin{array}{rcl}
C+W=38.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=34.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=72.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&72\div3\\
&=&24.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&38-24\\
&=&14.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume William answered all the 38 questions correctly, and each correct answer has 2 marks, then William should score 76 marks,
\begin{array}{rcl}
38\times2=76.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since William only scored 34 marks, therefore William totally lost
\begin{array}{rcl}
76-34=42.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
42\div3=14.
\end{array}
The number of correct answers is
\begin{array}{rcl}
38-14=24.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 38, we have,
\begin{array}{rcl}
C+W=38.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=34.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=72.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&72\div3\\
&=&24.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&38-24\\
&=&14.\tag{6}
\end{array}
Sophia attended a South-East Asia Maths Olympaid (SEAMO). Sophia answered all 40 questions. For each correct answer, Sophia will get 5 marks. However, for each wrong answer, Sophia will be deducted by 1 mark(s). If Sophia scored 80 marks in total, how many questions did Sophia answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Sophia answered all the 40 questions correctly, and each correct answer has 5 marks, then Sophia should score 200 marks,
\begin{array}{rcl}
40\times5=200.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Sophia only scored 80 marks, therefore Sophia totally lost
\begin{array}{rcl}
200-80=120.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
120\div6=20.
\end{array}
The number of correct answers is
\begin{array}{rcl}
40-20=20.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 40, we have,
\begin{array}{rcl}
C+W=40.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=80.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=120.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&120\div6\\
&=&20.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&40-20\\
&=&20.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Sophia answered all the 40 questions correctly, and each correct answer has 5 marks, then Sophia should score 200 marks,
\begin{array}{rcl}
40\times5=200.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Sophia only scored 80 marks, therefore Sophia totally lost
\begin{array}{rcl}
200-80=120.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
120\div6=20.
\end{array}
The number of correct answers is
\begin{array}{rcl}
40-20=20.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 40, we have,
\begin{array}{rcl}
C+W=40.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=80.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=120.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&120\div6\\
&=&20.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&40-20\\
&=&20.\tag{6}
\end{array}
Mason attended a Australian Maths Trust (AMT). Mason answered all 137 questions. For each correct answer, Mason will get 10 marks. However, for each wrong answer, Mason will be deducted by 2 mark(s). If Mason scored 170 marks in total, how many questions did Mason answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Mason answered all the 137 questions correctly, and each correct answer has 10 marks, then Mason should score 1370 marks,
\begin{array}{rcl}
137\times10=1370.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Mason only scored 170 marks, therefore Mason totally lost
\begin{array}{rcl}
1370-170=1200.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
1200\div12=100.
\end{array}
The number of correct answers is
\begin{array}{rcl}
137-100=37.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 137, we have,
\begin{array}{rcl}
C+W=137.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=170.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=274.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=444.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&444\div12\\
&=&37.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&137-37\\
&=&100.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Mason answered all the 137 questions correctly, and each correct answer has 10 marks, then Mason should score 1370 marks,
\begin{array}{rcl}
137\times10=1370.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Mason only scored 170 marks, therefore Mason totally lost
\begin{array}{rcl}
1370-170=1200.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
1200\div12=100.
\end{array}
The number of correct answers is
\begin{array}{rcl}
137-100=37.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 137, we have,
\begin{array}{rcl}
C+W=137.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=170.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=274.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=444.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&444\div12\\
&=&37.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&137-37\\
&=&100.\tag{6}
\end{array}
James attended a South-East Asia Maths Olympaid (SEAMO). James answered all 34 questions. For each correct answer, James will get 6 marks. However, for each wrong answer, James will be deducted by 2 mark(s). If James scored 108 marks in total, how many questions did James answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume James answered all the 34 questions correctly, and each correct answer has 6 marks, then James should score 204 marks,
\begin{array}{rcl}
34\times6=204.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since James only scored 108 marks, therefore James totally lost
\begin{array}{rcl}
204-108=96.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
96\div8=12.
\end{array}
The number of correct answers is
\begin{array}{rcl}
34-12=22.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 34, we have,
\begin{array}{rcl}
C+W=34.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=108.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=68.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=176.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&176\div8\\
&=&22.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&34-22\\
&=&12.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume James answered all the 34 questions correctly, and each correct answer has 6 marks, then James should score 204 marks,
\begin{array}{rcl}
34\times6=204.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since James only scored 108 marks, therefore James totally lost
\begin{array}{rcl}
204-108=96.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
96\div8=12.
\end{array}
The number of correct answers is
\begin{array}{rcl}
34-12=22.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 34, we have,
\begin{array}{rcl}
C+W=34.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=108.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=68.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=176.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&176\div8\\
&=&22.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&34-22\\
&=&12.\tag{6}
\end{array}
Noah attended a English Spelling Bee Competition. Noah answered all 12 questions. For each correct answer, Noah will get 3 marks. However, for each wrong answer, Noah will be deducted by 1 mark(s). If Noah scored 36 marks in total, how many questions did Noah answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Noah answered all the 12 questions correctly, and each correct answer has 3 marks, then Noah should score 36 marks,
\begin{array}{rcl}
12\times3=36.
\end{array}
For every question Noah answered wrongly, Noah will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Noah only scored 36 marks, therefore Noah totally lost
\begin{array}{rcl}
36-36=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div4=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
12-0=12.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 12, we have,
\begin{array}{rcl}
C+W=12.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=36.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=48.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&48\div4\\
&=&12.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&12-12\\
&=&0.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Noah answered all the 12 questions correctly, and each correct answer has 3 marks, then Noah should score 36 marks,
\begin{array}{rcl}
12\times3=36.
\end{array}
For every question Noah answered wrongly, Noah will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Noah only scored 36 marks, therefore Noah totally lost
\begin{array}{rcl}
36-36=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div4=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
12-0=12.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 12, we have,
\begin{array}{rcl}
C+W=12.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=36.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=48.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&48\div4\\
&=&12.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&12-12\\
&=&0.\tag{6}
\end{array}
Liam attended a South-East Asia Maths Olympaid (SEAMO). Liam answered all 11 questions. For each correct answer, Liam will get 4 marks. However, for each wrong answer, Liam will be deducted by 1 mark(s). If Liam scored 44 marks in total, how many questions did Liam answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Liam answered all the 11 questions correctly, and each correct answer has 4 marks, then Liam should score 44 marks,
\begin{array}{rcl}
11\times4=44.
\end{array}
For every question Liam answered wrongly, Liam will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Liam only scored 44 marks, therefore Liam totally lost
\begin{array}{rcl}
44-44=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div5=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
11-0=11.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 11, we have,
\begin{array}{rcl}
C+W=11.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=44.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=55.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&55\div5\\
&=&11.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&11-11\\
&=&0.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Liam answered all the 11 questions correctly, and each correct answer has 4 marks, then Liam should score 44 marks,
\begin{array}{rcl}
11\times4=44.
\end{array}
For every question Liam answered wrongly, Liam will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Liam only scored 44 marks, therefore Liam totally lost
\begin{array}{rcl}
44-44=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div5=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
11-0=11.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 11, we have,
\begin{array}{rcl}
C+W=11.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=44.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=55.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&55\div5\\
&=&11.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&11-11\\
&=&0.\tag{6}
\end{array}
James attended a Australian Maths Trust (AMT). James answered all 31 questions. For each correct answer, James will get 2 marks. However, for each wrong answer, James will be deducted by 1 mark(s). If James scored 26 marks in total, how many questions did James answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume James answered all the 31 questions correctly, and each correct answer has 2 marks, then James should score 62 marks,
\begin{array}{rcl}
31\times2=62.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since James only scored 26 marks, therefore James totally lost
\begin{array}{rcl}
62-26=36.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
36\div3=12.
\end{array}
The number of correct answers is
\begin{array}{rcl}
31-12=19.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 31, we have,
\begin{array}{rcl}
C+W=31.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=26.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=57.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&57\div3\\
&=&19.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&31-19\\
&=&12.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume James answered all the 31 questions correctly, and each correct answer has 2 marks, then James should score 62 marks,
\begin{array}{rcl}
31\times2=62.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since James only scored 26 marks, therefore James totally lost
\begin{array}{rcl}
62-26=36.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
36\div3=12.
\end{array}
The number of correct answers is
\begin{array}{rcl}
31-12=19.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 31, we have,
\begin{array}{rcl}
C+W=31.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=26.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=57.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&57\div3\\
&=&19.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&31-19\\
&=&12.\tag{6}
\end{array}
Sophia attended a Chinese Multiple Choices Test. Sophia answered all 34 questions. For each correct answer, Sophia will get 4 marks. However, for each wrong answer, Sophia will be deducted by 2 mark(s). If Sophia scored 40 marks in total, how many questions did Sophia answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Sophia answered all the 34 questions correctly, and each correct answer has 4 marks, then Sophia should score 136 marks,
\begin{array}{rcl}
34\times4=136.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Sophia only scored 40 marks, therefore Sophia totally lost
\begin{array}{rcl}
136-40=96.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
96\div6=16.
\end{array}
The number of correct answers is
\begin{array}{rcl}
34-16=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 34, we have,
\begin{array}{rcl}
C+W=34.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=40.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=68.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=108.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&108\div6\\
&=&18.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&34-18\\
&=&16.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Sophia answered all the 34 questions correctly, and each correct answer has 4 marks, then Sophia should score 136 marks,
\begin{array}{rcl}
34\times4=136.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Sophia only scored 40 marks, therefore Sophia totally lost
\begin{array}{rcl}
136-40=96.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
96\div6=16.
\end{array}
The number of correct answers is
\begin{array}{rcl}
34-16=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 34, we have,
\begin{array}{rcl}
C+W=34.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=40.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=68.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=108.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&108\div6\\
&=&18.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&34-18\\
&=&16.\tag{6}
\end{array}
Olivia attended a South-East Asia Maths Olympaid (SEAMO). Olivia answered all 26 questions. For each correct answer, Olivia will get 3 marks. However, for each wrong answer, Olivia will be deducted by 1 mark(s). If Olivia scored 54 marks in total, how many questions did Olivia answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Olivia answered all the 26 questions correctly, and each correct answer has 3 marks, then Olivia should score 78 marks,
\begin{array}{rcl}
26\times3=78.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Olivia only scored 54 marks, therefore Olivia totally lost
\begin{array}{rcl}
78-54=24.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
24\div4=6.
\end{array}
The number of correct answers is
\begin{array}{rcl}
26-6=20.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 26, we have,
\begin{array}{rcl}
C+W=26.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=54.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=80.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&80\div4\\
&=&20.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&26-20\\
&=&6.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Olivia answered all the 26 questions correctly, and each correct answer has 3 marks, then Olivia should score 78 marks,
\begin{array}{rcl}
26\times3=78.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Olivia only scored 54 marks, therefore Olivia totally lost
\begin{array}{rcl}
78-54=24.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
24\div4=6.
\end{array}
The number of correct answers is
\begin{array}{rcl}
26-6=20.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 26, we have,
\begin{array}{rcl}
C+W=26.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=54.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=80.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&80\div4\\
&=&20.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&26-20\\
&=&6.\tag{6}
\end{array}
Mason attended a Australian Maths Trust (AMT). Mason answered all 63 questions. For each correct answer, Mason will get 6 marks. However, for each wrong answer, Mason will be deducted by 2 mark(s). If Mason scored 90 marks in total, how many questions did Mason answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Mason answered all the 63 questions correctly, and each correct answer has 6 marks, then Mason should score 378 marks,
\begin{array}{rcl}
63\times6=378.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Mason only scored 90 marks, therefore Mason totally lost
\begin{array}{rcl}
378-90=288.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
288\div8=36.
\end{array}
The number of correct answers is
\begin{array}{rcl}
63-36=27.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 63, we have,
\begin{array}{rcl}
C+W=63.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=90.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=126.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=216.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&216\div8\\
&=&27.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&63-27\\
&=&36.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Mason answered all the 63 questions correctly, and each correct answer has 6 marks, then Mason should score 378 marks,
\begin{array}{rcl}
63\times6=378.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Mason only scored 90 marks, therefore Mason totally lost
\begin{array}{rcl}
378-90=288.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
288\div8=36.
\end{array}
The number of correct answers is
\begin{array}{rcl}
63-36=27.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 63, we have,
\begin{array}{rcl}
C+W=63.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=90.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=126.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=216.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&216\div8\\
&=&27.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&63-27\\
&=&36.\tag{6}
\end{array}
Ava attended a Chinese Multiple Choices Test. Ava answered all 134 questions. For each correct answer, Ava will get 10 marks. However, for each wrong answer, Ava will be deducted by 2 mark(s). If Ava scored 140 marks in total, how many questions did Ava answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Ava answered all the 134 questions correctly, and each correct answer has 10 marks, then Ava should score 1340 marks,
\begin{array}{rcl}
134\times10=1340.
\end{array}
For every question Ava answered wrongly, Ava will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Ava only scored 140 marks, therefore Ava totally lost
\begin{array}{rcl}
1340-140=1200.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
1200\div12=100.
\end{array}
The number of correct answers is
\begin{array}{rcl}
134-100=34.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 134, we have,
\begin{array}{rcl}
C+W=134.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=140.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=268.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=408.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&408\div12\\
&=&34.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&134-34\\
&=&100.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Ava answered all the 134 questions correctly, and each correct answer has 10 marks, then Ava should score 1340 marks,
\begin{array}{rcl}
134\times10=1340.
\end{array}
For every question Ava answered wrongly, Ava will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Ava only scored 140 marks, therefore Ava totally lost
\begin{array}{rcl}
1340-140=1200.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
1200\div12=100.
\end{array}
The number of correct answers is
\begin{array}{rcl}
134-100=34.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 134, we have,
\begin{array}{rcl}
C+W=134.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=140.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=268.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=408.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&408\div12\\
&=&34.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&134-34\\
&=&100.\tag{6}
\end{array}
Larry Page attended a South-East Asia Maths Olympaid (SEAMO). Larry Page answered all 12 questions. For each correct answer, Larry Page will get 3 marks. However, for each wrong answer, Larry Page will be deducted by 1 mark(s). If Larry Page scored 36 marks in total, how many questions did Larry Page answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Larry Page answered all the 12 questions correctly, and each correct answer has 3 marks, then Larry Page should score 36 marks,
\begin{array}{rcl}
12\times3=36.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Larry Page only scored 36 marks, therefore Larry Page totally lost
\begin{array}{rcl}
36-36=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div4=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
12-0=12.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 12, we have,
\begin{array}{rcl}
C+W=12.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=36.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=48.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&48\div4\\
&=&12.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&12-12\\
&=&0.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Larry Page answered all the 12 questions correctly, and each correct answer has 3 marks, then Larry Page should score 36 marks,
\begin{array}{rcl}
12\times3=36.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Larry Page only scored 36 marks, therefore Larry Page totally lost
\begin{array}{rcl}
36-36=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div4=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
12-0=12.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 12, we have,
\begin{array}{rcl}
C+W=12.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=36.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=48.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&48\div4\\
&=&12.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&12-12\\
&=&0.\tag{6}
\end{array}
Liam attended a Chinese Multiple Choices Test. Liam answered all 26 questions. For each correct answer, Liam will get 2 marks. However, for each wrong answer, Liam will be deducted by 1 mark(s). If Liam scored 40 marks in total, how many questions did Liam answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Liam answered all the 26 questions correctly, and each correct answer has 2 marks, then Liam should score 52 marks,
\begin{array}{rcl}
26\times2=52.
\end{array}
For every question Liam answered wrongly, Liam will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Liam only scored 40 marks, therefore Liam totally lost
\begin{array}{rcl}
52-40=12.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
12\div3=4.
\end{array}
The number of correct answers is
\begin{array}{rcl}
26-4=22.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 26, we have,
\begin{array}{rcl}
C+W=26.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=40.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=66.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&66\div3\\
&=&22.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&26-22\\
&=&4.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Liam answered all the 26 questions correctly, and each correct answer has 2 marks, then Liam should score 52 marks,
\begin{array}{rcl}
26\times2=52.
\end{array}
For every question Liam answered wrongly, Liam will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Liam only scored 40 marks, therefore Liam totally lost
\begin{array}{rcl}
52-40=12.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
12\div3=4.
\end{array}
The number of correct answers is
\begin{array}{rcl}
26-4=22.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 26, we have,
\begin{array}{rcl}
C+W=26.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=40.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=66.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&66\div3\\
&=&22.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&26-22\\
&=&4.\tag{6}
\end{array}
James attended a English Spelling Bee Competition. James answered all 43 questions. For each correct answer, James will get 8 marks. However, for each wrong answer, James will be deducted by 2 mark(s). If James scored 104 marks in total, how many questions did James answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume James answered all the 43 questions correctly, and each correct answer has 8 marks, then James should score 344 marks,
\begin{array}{rcl}
43\times8=344.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since James only scored 104 marks, therefore James totally lost
\begin{array}{rcl}
344-104=240.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
240\div10=24.
\end{array}
The number of correct answers is
\begin{array}{rcl}
43-24=19.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 43, we have,
\begin{array}{rcl}
C+W=43.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=104.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=86.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=190.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&190\div10\\
&=&19.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&43-19\\
&=&24.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume James answered all the 43 questions correctly, and each correct answer has 8 marks, then James should score 344 marks,
\begin{array}{rcl}
43\times8=344.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since James only scored 104 marks, therefore James totally lost
\begin{array}{rcl}
344-104=240.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
240\div10=24.
\end{array}
The number of correct answers is
\begin{array}{rcl}
43-24=19.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 43, we have,
\begin{array}{rcl}
C+W=43.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=104.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=86.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=190.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&190\div10\\
&=&19.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&43-19\\
&=&24.\tag{6}
\end{array}
Ava attended a English Spelling Bee Competition. Ava answered all 32 questions. For each correct answer, Ava will get 2 marks. However, for each wrong answer, Ava will be deducted by 1 mark(s). If Ava scored 22 marks in total, how many questions did Ava answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Ava answered all the 32 questions correctly, and each correct answer has 2 marks, then Ava should score 64 marks,
\begin{array}{rcl}
32\times2=64.
\end{array}
For every question Ava answered wrongly, Ava will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Ava only scored 22 marks, therefore Ava totally lost
\begin{array}{rcl}
64-22=42.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
42\div3=14.
\end{array}
The number of correct answers is
\begin{array}{rcl}
32-14=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 32, we have,
\begin{array}{rcl}
C+W=32.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=22.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=54.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&54\div3\\
&=&18.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&32-18\\
&=&14.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Ava answered all the 32 questions correctly, and each correct answer has 2 marks, then Ava should score 64 marks,
\begin{array}{rcl}
32\times2=64.
\end{array}
For every question Ava answered wrongly, Ava will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Ava only scored 22 marks, therefore Ava totally lost
\begin{array}{rcl}
64-22=42.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
42\div3=14.
\end{array}
The number of correct answers is
\begin{array}{rcl}
32-14=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 32, we have,
\begin{array}{rcl}
C+W=32.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=22.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=54.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&54\div3\\
&=&18.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&32-18\\
&=&14.\tag{6}
\end{array}
Sophia attended a Chinese Multiple Choices Test. Sophia answered all 18 questions. For each correct answer, Sophia will get 3 marks. However, for each wrong answer, Sophia will be deducted by 1 mark(s). If Sophia scored 54 marks in total, how many questions did Sophia answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Sophia answered all the 18 questions correctly, and each correct answer has 3 marks, then Sophia should score 54 marks,
\begin{array}{rcl}
18\times3=54.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Sophia only scored 54 marks, therefore Sophia totally lost
\begin{array}{rcl}
54-54=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div4=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
18-0=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 18, we have,
\begin{array}{rcl}
C+W=18.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=54.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=72.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&72\div4\\
&=&18.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&18-18\\
&=&0.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Sophia answered all the 18 questions correctly, and each correct answer has 3 marks, then Sophia should score 54 marks,
\begin{array}{rcl}
18\times3=54.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Sophia only scored 54 marks, therefore Sophia totally lost
\begin{array}{rcl}
54-54=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div4=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
18-0=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 18, we have,
\begin{array}{rcl}
C+W=18.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=54.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=72.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&72\div4\\
&=&18.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&18-18\\
&=&0.\tag{6}
\end{array}
Emma attended a American Maths Olympiad (AMO). Emma answered all 30 questions. For each correct answer, Emma will get 4 marks. However, for each wrong answer, Emma will be deducted by 1 mark(s). If Emma scored 80 marks in total, how many questions did Emma answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Emma answered all the 30 questions correctly, and each correct answer has 4 marks, then Emma should score 120 marks,
\begin{array}{rcl}
30\times4=120.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Emma only scored 80 marks, therefore Emma totally lost
\begin{array}{rcl}
120-80=40.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
40\div5=8.
\end{array}
The number of correct answers is
\begin{array}{rcl}
30-8=22.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 30, we have,
\begin{array}{rcl}
C+W=30.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=80.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=110.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&110\div5\\
&=&22.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&30-22\\
&=&8.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Emma answered all the 30 questions correctly, and each correct answer has 4 marks, then Emma should score 120 marks,
\begin{array}{rcl}
30\times4=120.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Emma only scored 80 marks, therefore Emma totally lost
\begin{array}{rcl}
120-80=40.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
40\div5=8.
\end{array}
The number of correct answers is
\begin{array}{rcl}
30-8=22.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 30, we have,
\begin{array}{rcl}
C+W=30.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=80.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=110.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&110\div5\\
&=&22.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&30-22\\
&=&8.\tag{6}
\end{array}
Mason attended a Australian Maths Trust (AMT). Mason answered all 40 questions. For each correct answer, Mason will get 8 marks. However, for each wrong answer, Mason will be deducted by 2 mark(s). If Mason scored 160 marks in total, how many questions did Mason answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Mason answered all the 40 questions correctly, and each correct answer has 8 marks, then Mason should score 320 marks,
\begin{array}{rcl}
40\times8=320.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Mason only scored 160 marks, therefore Mason totally lost
\begin{array}{rcl}
320-160=160.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
160\div10=16.
\end{array}
The number of correct answers is
\begin{array}{rcl}
40-16=24.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 40, we have,
\begin{array}{rcl}
C+W=40.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=160.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=80.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=240.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&240\div10\\
&=&24.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&40-24\\
&=&16.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Mason answered all the 40 questions correctly, and each correct answer has 8 marks, then Mason should score 320 marks,
\begin{array}{rcl}
40\times8=320.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Mason only scored 160 marks, therefore Mason totally lost
\begin{array}{rcl}
320-160=160.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
160\div10=16.
\end{array}
The number of correct answers is
\begin{array}{rcl}
40-16=24.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 40, we have,
\begin{array}{rcl}
C+W=40.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=160.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=80.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=240.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&240\div10\\
&=&24.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&40-24\\
&=&16.\tag{6}
\end{array}
Bill Gates attended a South-East Asia Maths Olympaid (SEAMO). Bill Gates answered all 26 questions. For each correct answer, Bill Gates will get 3 marks. However, for each wrong answer, Bill Gates will be deducted by 1 mark(s). If Bill Gates scored 42 marks in total, how many questions did Bill Gates answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Bill Gates answered all the 26 questions correctly, and each correct answer has 3 marks, then Bill Gates should score 78 marks,
\begin{array}{rcl}
26\times3=78.
\end{array}
For every question Bill Gates answered wrongly, Bill Gates will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Bill Gates only scored 42 marks, therefore Bill Gates totally lost
\begin{array}{rcl}
78-42=36.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
36\div4=9.
\end{array}
The number of correct answers is
\begin{array}{rcl}
26-9=17.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 26, we have,
\begin{array}{rcl}
C+W=26.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=42.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=68.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&68\div4\\
&=&17.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&26-17\\
&=&9.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Bill Gates answered all the 26 questions correctly, and each correct answer has 3 marks, then Bill Gates should score 78 marks,
\begin{array}{rcl}
26\times3=78.
\end{array}
For every question Bill Gates answered wrongly, Bill Gates will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Bill Gates only scored 42 marks, therefore Bill Gates totally lost
\begin{array}{rcl}
78-42=36.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
36\div4=9.
\end{array}
The number of correct answers is
\begin{array}{rcl}
26-9=17.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 26, we have,
\begin{array}{rcl}
C+W=26.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=42.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=68.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&68\div4\\
&=&17.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&26-17\\
&=&9.\tag{6}
\end{array}
Mason attended a Australian Maths Trust (AMT). Mason answered all 40 questions. For each correct answer, Mason will get 3 marks. However, for each wrong answer, Mason will be deducted by 1 mark(s). If Mason scored 48 marks in total, how many questions did Mason answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Mason answered all the 40 questions correctly, and each correct answer has 3 marks, then Mason should score 120 marks,
\begin{array}{rcl}
40\times3=120.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Mason only scored 48 marks, therefore Mason totally lost
\begin{array}{rcl}
120-48=72.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
72\div4=18.
\end{array}
The number of correct answers is
\begin{array}{rcl}
40-18=22.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 40, we have,
\begin{array}{rcl}
C+W=40.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=48.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=88.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&88\div4\\
&=&22.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&40-22\\
&=&18.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Mason answered all the 40 questions correctly, and each correct answer has 3 marks, then Mason should score 120 marks,
\begin{array}{rcl}
40\times3=120.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Mason only scored 48 marks, therefore Mason totally lost
\begin{array}{rcl}
120-48=72.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
72\div4=18.
\end{array}
The number of correct answers is
\begin{array}{rcl}
40-18=22.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 40, we have,
\begin{array}{rcl}
C+W=40.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=48.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=88.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&88\div4\\
&=&22.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&40-22\\
&=&18.\tag{6}
\end{array}
William attended a American Maths Olympiad (AMO). William answered all 51 questions. For each correct answer, William will get 3 marks. However, for each wrong answer, William will be deducted by 1 mark(s). If William scored 45 marks in total, how many questions did William answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume William answered all the 51 questions correctly, and each correct answer has 3 marks, then William should score 153 marks,
\begin{array}{rcl}
51\times3=153.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since William only scored 45 marks, therefore William totally lost
\begin{array}{rcl}
153-45=108.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
108\div4=27.
\end{array}
The number of correct answers is
\begin{array}{rcl}
51-27=24.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 51, we have,
\begin{array}{rcl}
C+W=51.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=45.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=96.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&96\div4\\
&=&24.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&51-24\\
&=&27.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume William answered all the 51 questions correctly, and each correct answer has 3 marks, then William should score 153 marks,
\begin{array}{rcl}
51\times3=153.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since William only scored 45 marks, therefore William totally lost
\begin{array}{rcl}
153-45=108.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
108\div4=27.
\end{array}
The number of correct answers is
\begin{array}{rcl}
51-27=24.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 51, we have,
\begin{array}{rcl}
C+W=51.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=45.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=96.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&96\div4\\
&=&24.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&51-24\\
&=&27.\tag{6}
\end{array}
Mason attended a English Spelling Bee Competition. Mason answered all 63 questions. For each correct answer, Mason will get 4 marks. However, for each wrong answer, Mason will be deducted by 2 mark(s). If Mason scored 60 marks in total, how many questions did Mason answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Mason answered all the 63 questions correctly, and each correct answer has 4 marks, then Mason should score 252 marks,
\begin{array}{rcl}
63\times4=252.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Mason only scored 60 marks, therefore Mason totally lost
\begin{array}{rcl}
252-60=192.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
192\div6=32.
\end{array}
The number of correct answers is
\begin{array}{rcl}
63-32=31.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 63, we have,
\begin{array}{rcl}
C+W=63.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=60.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=126.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=186.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&186\div6\\
&=&31.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&63-31\\
&=&32.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Mason answered all the 63 questions correctly, and each correct answer has 4 marks, then Mason should score 252 marks,
\begin{array}{rcl}
63\times4=252.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Mason only scored 60 marks, therefore Mason totally lost
\begin{array}{rcl}
252-60=192.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
192\div6=32.
\end{array}
The number of correct answers is
\begin{array}{rcl}
63-32=31.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 63, we have,
\begin{array}{rcl}
C+W=63.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=60.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=126.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=186.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&186\div6\\
&=&31.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&63-31\\
&=&32.\tag{6}
\end{array}
Sophia attended a English Spelling Bee Competition. Sophia answered all 132 questions. For each correct answer, Sophia will get 10 marks. However, for each wrong answer, Sophia will be deducted by 2 mark(s). If Sophia scored 120 marks in total, how many questions did Sophia answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Sophia answered all the 132 questions correctly, and each correct answer has 10 marks, then Sophia should score 1320 marks,
\begin{array}{rcl}
132\times10=1320.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Sophia only scored 120 marks, therefore Sophia totally lost
\begin{array}{rcl}
1320-120=1200.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
1200\div12=100.
\end{array}
The number of correct answers is
\begin{array}{rcl}
132-100=32.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 132, we have,
\begin{array}{rcl}
C+W=132.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=120.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=264.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=384.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&384\div12\\
&=&32.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&132-32\\
&=&100.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Sophia answered all the 132 questions correctly, and each correct answer has 10 marks, then Sophia should score 1320 marks,
\begin{array}{rcl}
132\times10=1320.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Sophia only scored 120 marks, therefore Sophia totally lost
\begin{array}{rcl}
1320-120=1200.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
1200\div12=100.
\end{array}
The number of correct answers is
\begin{array}{rcl}
132-100=32.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 132, we have,
\begin{array}{rcl}
C+W=132.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=120.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=264.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=384.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&384\div12\\
&=&32.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&132-32\\
&=&100.\tag{6}
\end{array}
Larry Page attended a American Maths Olympiad (AMO). Larry Page answered all 49 questions. For each correct answer, Larry Page will get 5 marks. However, for each wrong answer, Larry Page will be deducted by 1 mark(s). If Larry Page scored 65 marks in total, how many questions did Larry Page answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Larry Page answered all the 49 questions correctly, and each correct answer has 5 marks, then Larry Page should score 245 marks,
\begin{array}{rcl}
49\times5=245.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Larry Page only scored 65 marks, therefore Larry Page totally lost
\begin{array}{rcl}
245-65=180.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
180\div6=30.
\end{array}
The number of correct answers is
\begin{array}{rcl}
49-30=19.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 49, we have,
\begin{array}{rcl}
C+W=49.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=65.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=114.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&114\div6\\
&=&19.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&49-19\\
&=&30.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Larry Page answered all the 49 questions correctly, and each correct answer has 5 marks, then Larry Page should score 245 marks,
\begin{array}{rcl}
49\times5=245.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Larry Page only scored 65 marks, therefore Larry Page totally lost
\begin{array}{rcl}
245-65=180.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
180\div6=30.
\end{array}
The number of correct answers is
\begin{array}{rcl}
49-30=19.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 49, we have,
\begin{array}{rcl}
C+W=49.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=65.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=114.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&114\div6\\
&=&19.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&49-19\\
&=&30.\tag{6}
\end{array}
Mason attended a English Spelling Bee Competition. Mason answered all 41 questions. For each correct answer, Mason will get 2 marks. However, for each wrong answer, Mason will be deducted by 1 mark(s). If Mason scored 34 marks in total, how many questions did Mason answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Mason answered all the 41 questions correctly, and each correct answer has 2 marks, then Mason should score 82 marks,
\begin{array}{rcl}
41\times2=82.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Mason only scored 34 marks, therefore Mason totally lost
\begin{array}{rcl}
82-34=48.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
48\div3=16.
\end{array}
The number of correct answers is
\begin{array}{rcl}
41-16=25.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 41, we have,
\begin{array}{rcl}
C+W=41.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=34.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=75.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&75\div3\\
&=&25.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&41-25\\
&=&16.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Mason answered all the 41 questions correctly, and each correct answer has 2 marks, then Mason should score 82 marks,
\begin{array}{rcl}
41\times2=82.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Mason only scored 34 marks, therefore Mason totally lost
\begin{array}{rcl}
82-34=48.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
48\div3=16.
\end{array}
The number of correct answers is
\begin{array}{rcl}
41-16=25.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 41, we have,
\begin{array}{rcl}
C+W=41.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=34.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=75.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&75\div3\\
&=&25.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&41-25\\
&=&16.\tag{6}
\end{array}
Jacob attended a American Maths Olympiad (AMO). Jacob answered all 71 questions. For each correct answer, Jacob will get 5 marks. However, for each wrong answer, Jacob will be deducted by 1 mark(s). If Jacob scored 55 marks in total, how many questions did Jacob answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Jacob answered all the 71 questions correctly, and each correct answer has 5 marks, then Jacob should score 355 marks,
\begin{array}{rcl}
71\times5=355.
\end{array}
For every question Jacob answered wrongly, Jacob will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Jacob only scored 55 marks, therefore Jacob totally lost
\begin{array}{rcl}
355-55=300.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
300\div6=50.
\end{array}
The number of correct answers is
\begin{array}{rcl}
71-50=21.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 71, we have,
\begin{array}{rcl}
C+W=71.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=55.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=126.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&126\div6\\
&=&21.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&71-21\\
&=&50.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Jacob answered all the 71 questions correctly, and each correct answer has 5 marks, then Jacob should score 355 marks,
\begin{array}{rcl}
71\times5=355.
\end{array}
For every question Jacob answered wrongly, Jacob will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Jacob only scored 55 marks, therefore Jacob totally lost
\begin{array}{rcl}
355-55=300.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
300\div6=50.
\end{array}
The number of correct answers is
\begin{array}{rcl}
71-50=21.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 71, we have,
\begin{array}{rcl}
C+W=71.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=55.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=126.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&126\div6\\
&=&21.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&71-21\\
&=&50.\tag{6}
\end{array}
James attended a Australian Maths Trust (AMT). James answered all 38 questions. For each correct answer, James will get 4 marks. However, for each wrong answer, James will be deducted by 2 mark(s). If James scored 80 marks in total, how many questions did James answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume James answered all the 38 questions correctly, and each correct answer has 4 marks, then James should score 152 marks,
\begin{array}{rcl}
38\times4=152.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since James only scored 80 marks, therefore James totally lost
\begin{array}{rcl}
152-80=72.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
72\div6=12.
\end{array}
The number of correct answers is
\begin{array}{rcl}
38-12=26.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 38, we have,
\begin{array}{rcl}
C+W=38.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=80.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=76.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=156.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&156\div6\\
&=&26.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&38-26\\
&=&12.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume James answered all the 38 questions correctly, and each correct answer has 4 marks, then James should score 152 marks,
\begin{array}{rcl}
38\times4=152.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since James only scored 80 marks, therefore James totally lost
\begin{array}{rcl}
152-80=72.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
72\div6=12.
\end{array}
The number of correct answers is
\begin{array}{rcl}
38-12=26.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 38, we have,
\begin{array}{rcl}
C+W=38.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=80.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=76.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=156.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&156\div6\\
&=&26.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&38-26\\
&=&12.\tag{6}
\end{array}
Larry Page attended a South-East Asia Maths Olympaid (SEAMO). Larry Page answered all 67 questions. For each correct answer, Larry Page will get 4 marks. However, for each wrong answer, Larry Page will be deducted by 2 mark(s). If Larry Page scored 76 marks in total, how many questions did Larry Page answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Larry Page answered all the 67 questions correctly, and each correct answer has 4 marks, then Larry Page should score 268 marks,
\begin{array}{rcl}
67\times4=268.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Larry Page only scored 76 marks, therefore Larry Page totally lost
\begin{array}{rcl}
268-76=192.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
192\div6=32.
\end{array}
The number of correct answers is
\begin{array}{rcl}
67-32=35.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 67, we have,
\begin{array}{rcl}
C+W=67.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=76.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=134.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=210.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&210\div6\\
&=&35.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&67-35\\
&=&32.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Larry Page answered all the 67 questions correctly, and each correct answer has 4 marks, then Larry Page should score 268 marks,
\begin{array}{rcl}
67\times4=268.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Larry Page only scored 76 marks, therefore Larry Page totally lost
\begin{array}{rcl}
268-76=192.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
192\div6=32.
\end{array}
The number of correct answers is
\begin{array}{rcl}
67-32=35.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 67, we have,
\begin{array}{rcl}
C+W=67.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=76.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=134.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=210.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&210\div6\\
&=&35.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&67-35\\
&=&32.\tag{6}
\end{array}
Sophia attended a English Spelling Bee Competition. Sophia answered all 28 questions. For each correct answer, Sophia will get 2 marks. However, for each wrong answer, Sophia will be deducted by 1 mark(s). If Sophia scored 26 marks in total, how many questions did Sophia answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Sophia answered all the 28 questions correctly, and each correct answer has 2 marks, then Sophia should score 56 marks,
\begin{array}{rcl}
28\times2=56.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Sophia only scored 26 marks, therefore Sophia totally lost
\begin{array}{rcl}
56-26=30.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
30\div3=10.
\end{array}
The number of correct answers is
\begin{array}{rcl}
28-10=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 28, we have,
\begin{array}{rcl}
C+W=28.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=26.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=54.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&54\div3\\
&=&18.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&28-18\\
&=&10.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Sophia answered all the 28 questions correctly, and each correct answer has 2 marks, then Sophia should score 56 marks,
\begin{array}{rcl}
28\times2=56.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Sophia only scored 26 marks, therefore Sophia totally lost
\begin{array}{rcl}
56-26=30.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
30\div3=10.
\end{array}
The number of correct answers is
\begin{array}{rcl}
28-10=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 28, we have,
\begin{array}{rcl}
C+W=28.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=26.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=54.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&54\div3\\
&=&18.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&28-18\\
&=&10.\tag{6}
\end{array}
Emma attended a South-East Asia Maths Olympaid (SEAMO). Emma answered all 48 questions. For each correct answer, Emma will get 10 marks. However, for each wrong answer, Emma will be deducted by 2 mark(s). If Emma scored 120 marks in total, how many questions did Emma answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Emma answered all the 48 questions correctly, and each correct answer has 10 marks, then Emma should score 480 marks,
\begin{array}{rcl}
48\times10=480.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Emma only scored 120 marks, therefore Emma totally lost
\begin{array}{rcl}
480-120=360.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
360\div12=30.
\end{array}
The number of correct answers is
\begin{array}{rcl}
48-30=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 48, we have,
\begin{array}{rcl}
C+W=48.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=120.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=96.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=216.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&216\div12\\
&=&18.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&48-18\\
&=&30.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Emma answered all the 48 questions correctly, and each correct answer has 10 marks, then Emma should score 480 marks,
\begin{array}{rcl}
48\times10=480.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Emma only scored 120 marks, therefore Emma totally lost
\begin{array}{rcl}
480-120=360.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
360\div12=30.
\end{array}
The number of correct answers is
\begin{array}{rcl}
48-30=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 48, we have,
\begin{array}{rcl}
C+W=48.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=120.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=96.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=216.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&216\div12\\
&=&18.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&48-18\\
&=&30.\tag{6}
\end{array}
William attended a Chinese Multiple Choices Test. William answered all 73 questions. For each correct answer, William will get 8 marks. However, for each wrong answer, William will be deducted by 2 mark(s). If William scored 104 marks in total, how many questions did William answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume William answered all the 73 questions correctly, and each correct answer has 8 marks, then William should score 584 marks,
\begin{array}{rcl}
73\times8=584.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since William only scored 104 marks, therefore William totally lost
\begin{array}{rcl}
584-104=480.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
480\div10=48.
\end{array}
The number of correct answers is
\begin{array}{rcl}
73-48=25.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 73, we have,
\begin{array}{rcl}
C+W=73.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=104.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=146.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=250.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&250\div10\\
&=&25.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&73-25\\
&=&48.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume William answered all the 73 questions correctly, and each correct answer has 8 marks, then William should score 584 marks,
\begin{array}{rcl}
73\times8=584.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since William only scored 104 marks, therefore William totally lost
\begin{array}{rcl}
584-104=480.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
480\div10=48.
\end{array}
The number of correct answers is
\begin{array}{rcl}
73-48=25.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 73, we have,
\begin{array}{rcl}
C+W=73.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=104.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=146.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=250.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&250\div10\\
&=&25.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&73-25\\
&=&48.\tag{6}
\end{array}
William attended a Australian Maths Trust (AMT). William answered all 49 questions. For each correct answer, William will get 4 marks. However, for each wrong answer, William will be deducted by 2 mark(s). If William scored 76 marks in total, how many questions did William answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume William answered all the 49 questions correctly, and each correct answer has 4 marks, then William should score 196 marks,
\begin{array}{rcl}
49\times4=196.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since William only scored 76 marks, therefore William totally lost
\begin{array}{rcl}
196-76=120.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
120\div6=20.
\end{array}
The number of correct answers is
\begin{array}{rcl}
49-20=29.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 49, we have,
\begin{array}{rcl}
C+W=49.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=76.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=98.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=174.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&174\div6\\
&=&29.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&49-29\\
&=&20.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume William answered all the 49 questions correctly, and each correct answer has 4 marks, then William should score 196 marks,
\begin{array}{rcl}
49\times4=196.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since William only scored 76 marks, therefore William totally lost
\begin{array}{rcl}
196-76=120.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
120\div6=20.
\end{array}
The number of correct answers is
\begin{array}{rcl}
49-20=29.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 49, we have,
\begin{array}{rcl}
C+W=49.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=76.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=98.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=174.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&174\div6\\
&=&29.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&49-29\\
&=&20.\tag{6}
\end{array}
Olivia attended a American Maths Olympiad (AMO). Olivia answered all 138 questions. For each correct answer, Olivia will get 10 marks. However, for each wrong answer, Olivia will be deducted by 2 mark(s). If Olivia scored 180 marks in total, how many questions did Olivia answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Olivia answered all the 138 questions correctly, and each correct answer has 10 marks, then Olivia should score 1380 marks,
\begin{array}{rcl}
138\times10=1380.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Olivia only scored 180 marks, therefore Olivia totally lost
\begin{array}{rcl}
1380-180=1200.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
1200\div12=100.
\end{array}
The number of correct answers is
\begin{array}{rcl}
138-100=38.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 138, we have,
\begin{array}{rcl}
C+W=138.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=180.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=276.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=456.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&456\div12\\
&=&38.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&138-38\\
&=&100.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Olivia answered all the 138 questions correctly, and each correct answer has 10 marks, then Olivia should score 1380 marks,
\begin{array}{rcl}
138\times10=1380.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Olivia only scored 180 marks, therefore Olivia totally lost
\begin{array}{rcl}
1380-180=1200.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
1200\div12=100.
\end{array}
The number of correct answers is
\begin{array}{rcl}
138-100=38.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 138, we have,
\begin{array}{rcl}
C+W=138.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=180.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=276.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=456.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&456\div12\\
&=&38.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&138-38\\
&=&100.\tag{6}
\end{array}
Noah attended a Maths Competition. Noah answered all 21 questions. For each correct answer, Noah will get 4 marks. However, for each wrong answer, Noah will be deducted by 1 mark(s). If Noah scored 44 marks in total, how many questions did Noah answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Noah answered all the 21 questions correctly, and each correct answer has 4 marks, then Noah should score 84 marks,
\begin{array}{rcl}
21\times4=84.
\end{array}
For every question Noah answered wrongly, Noah will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Noah only scored 44 marks, therefore Noah totally lost
\begin{array}{rcl}
84-44=40.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
40\div5=8.
\end{array}
The number of correct answers is
\begin{array}{rcl}
21-8=13.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 21, we have,
\begin{array}{rcl}
C+W=21.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=44.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=65.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&65\div5\\
&=&13.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&21-13\\
&=&8.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Noah answered all the 21 questions correctly, and each correct answer has 4 marks, then Noah should score 84 marks,
\begin{array}{rcl}
21\times4=84.
\end{array}
For every question Noah answered wrongly, Noah will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Noah only scored 44 marks, therefore Noah totally lost
\begin{array}{rcl}
84-44=40.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
40\div5=8.
\end{array}
The number of correct answers is
\begin{array}{rcl}
21-8=13.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 21, we have,
\begin{array}{rcl}
C+W=21.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=44.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=65.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&65\div5\\
&=&13.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&21-13\\
&=&8.\tag{6}
\end{array}
William attended a Australian Maths Trust (AMT). William answered all 22 questions. For each correct answer, William will get 6 marks. However, for each wrong answer, William will be deducted by 2 mark(s). If William scored 84 marks in total, how many questions did William answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume William answered all the 22 questions correctly, and each correct answer has 6 marks, then William should score 132 marks,
\begin{array}{rcl}
22\times6=132.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since William only scored 84 marks, therefore William totally lost
\begin{array}{rcl}
132-84=48.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
48\div8=6.
\end{array}
The number of correct answers is
\begin{array}{rcl}
22-6=16.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 22, we have,
\begin{array}{rcl}
C+W=22.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=84.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=44.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=128.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&128\div8\\
&=&16.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&22-16\\
&=&6.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume William answered all the 22 questions correctly, and each correct answer has 6 marks, then William should score 132 marks,
\begin{array}{rcl}
22\times6=132.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since William only scored 84 marks, therefore William totally lost
\begin{array}{rcl}
132-84=48.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
48\div8=6.
\end{array}
The number of correct answers is
\begin{array}{rcl}
22-6=16.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 22, we have,
\begin{array}{rcl}
C+W=22.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=84.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=44.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=128.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&128\div8\\
&=&16.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&22-16\\
&=&6.\tag{6}
\end{array}
Bill Gates attended a Chinese Multiple Choices Test. Bill Gates answered all 38 questions. For each correct answer, Bill Gates will get 2 marks. However, for each wrong answer, Bill Gates will be deducted by 1 mark(s). If Bill Gates scored 40 marks in total, how many questions did Bill Gates answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Bill Gates answered all the 38 questions correctly, and each correct answer has 2 marks, then Bill Gates should score 76 marks,
\begin{array}{rcl}
38\times2=76.
\end{array}
For every question Bill Gates answered wrongly, Bill Gates will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Bill Gates only scored 40 marks, therefore Bill Gates totally lost
\begin{array}{rcl}
76-40=36.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
36\div3=12.
\end{array}
The number of correct answers is
\begin{array}{rcl}
38-12=26.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 38, we have,
\begin{array}{rcl}
C+W=38.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=40.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=78.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&78\div3\\
&=&26.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&38-26\\
&=&12.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Bill Gates answered all the 38 questions correctly, and each correct answer has 2 marks, then Bill Gates should score 76 marks,
\begin{array}{rcl}
38\times2=76.
\end{array}
For every question Bill Gates answered wrongly, Bill Gates will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Bill Gates only scored 40 marks, therefore Bill Gates totally lost
\begin{array}{rcl}
76-40=36.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
36\div3=12.
\end{array}
The number of correct answers is
\begin{array}{rcl}
38-12=26.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 38, we have,
\begin{array}{rcl}
C+W=38.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=40.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=78.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&78\div3\\
&=&26.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&38-26\\
&=&12.\tag{6}
\end{array}
Emma attended a Maths Competition. Emma answered all 67 questions. For each correct answer, Emma will get 4 marks. However, for each wrong answer, Emma will be deducted by 2 mark(s). If Emma scored 76 marks in total, how many questions did Emma answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Emma answered all the 67 questions correctly, and each correct answer has 4 marks, then Emma should score 268 marks,
\begin{array}{rcl}
67\times4=268.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Emma only scored 76 marks, therefore Emma totally lost
\begin{array}{rcl}
268-76=192.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
192\div6=32.
\end{array}
The number of correct answers is
\begin{array}{rcl}
67-32=35.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 67, we have,
\begin{array}{rcl}
C+W=67.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=76.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=134.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=210.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&210\div6\\
&=&35.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&67-35\\
&=&32.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Emma answered all the 67 questions correctly, and each correct answer has 4 marks, then Emma should score 268 marks,
\begin{array}{rcl}
67\times4=268.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Emma only scored 76 marks, therefore Emma totally lost
\begin{array}{rcl}
268-76=192.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
192\div6=32.
\end{array}
The number of correct answers is
\begin{array}{rcl}
67-32=35.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 67, we have,
\begin{array}{rcl}
C+W=67.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=76.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=134.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=210.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&210\div6\\
&=&35.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&67-35\\
&=&32.\tag{6}
\end{array}
Benjamin attended a English Spelling Bee Competition. Benjamin answered all 54 questions. For each correct answer, Benjamin will get 4 marks. However, for each wrong answer, Benjamin will be deducted by 2 mark(s). If Benjamin scored 72 marks in total, how many questions did Benjamin answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Benjamin answered all the 54 questions correctly, and each correct answer has 4 marks, then Benjamin should score 216 marks,
\begin{array}{rcl}
54\times4=216.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Benjamin only scored 72 marks, therefore Benjamin totally lost
\begin{array}{rcl}
216-72=144.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
144\div6=24.
\end{array}
The number of correct answers is
\begin{array}{rcl}
54-24=30.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 54, we have,
\begin{array}{rcl}
C+W=54.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=72.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=108.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=180.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&180\div6\\
&=&30.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&54-30\\
&=&24.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Benjamin answered all the 54 questions correctly, and each correct answer has 4 marks, then Benjamin should score 216 marks,
\begin{array}{rcl}
54\times4=216.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Benjamin only scored 72 marks, therefore Benjamin totally lost
\begin{array}{rcl}
216-72=144.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
144\div6=24.
\end{array}
The number of correct answers is
\begin{array}{rcl}
54-24=30.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 54, we have,
\begin{array}{rcl}
C+W=54.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=72.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=108.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=180.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&180\div6\\
&=&30.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&54-30\\
&=&24.\tag{6}
\end{array}
James attended a South-East Asia Maths Olympaid (SEAMO). James answered all 67 questions. For each correct answer, James will get 5 marks. However, for each wrong answer, James will be deducted by 1 mark(s). If James scored 95 marks in total, how many questions did James answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume James answered all the 67 questions correctly, and each correct answer has 5 marks, then James should score 335 marks,
\begin{array}{rcl}
67\times5=335.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since James only scored 95 marks, therefore James totally lost
\begin{array}{rcl}
335-95=240.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
240\div6=40.
\end{array}
The number of correct answers is
\begin{array}{rcl}
67-40=27.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 67, we have,
\begin{array}{rcl}
C+W=67.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=95.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=162.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&162\div6\\
&=&27.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&67-27\\
&=&40.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume James answered all the 67 questions correctly, and each correct answer has 5 marks, then James should score 335 marks,
\begin{array}{rcl}
67\times5=335.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since James only scored 95 marks, therefore James totally lost
\begin{array}{rcl}
335-95=240.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
240\div6=40.
\end{array}
The number of correct answers is
\begin{array}{rcl}
67-40=27.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 67, we have,
\begin{array}{rcl}
C+W=67.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=95.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=162.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&162\div6\\
&=&27.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&67-27\\
&=&40.\tag{6}
\end{array}
Isabella attended a English Spelling Bee Competition. Isabella answered all 16 questions. For each correct answer, Isabella will get 4 marks. However, for each wrong answer, Isabella will be deducted by 2 mark(s). If Isabella scored 40 marks in total, how many questions did Isabella answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Isabella answered all the 16 questions correctly, and each correct answer has 4 marks, then Isabella should score 64 marks,
\begin{array}{rcl}
16\times4=64.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Isabella only scored 40 marks, therefore Isabella totally lost
\begin{array}{rcl}
64-40=24.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
24\div6=4.
\end{array}
The number of correct answers is
\begin{array}{rcl}
16-4=12.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 16, we have,
\begin{array}{rcl}
C+W=16.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=40.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=32.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=72.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&72\div6\\
&=&12.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&16-12\\
&=&4.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Isabella answered all the 16 questions correctly, and each correct answer has 4 marks, then Isabella should score 64 marks,
\begin{array}{rcl}
16\times4=64.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Isabella only scored 40 marks, therefore Isabella totally lost
\begin{array}{rcl}
64-40=24.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
24\div6=4.
\end{array}
The number of correct answers is
\begin{array}{rcl}
16-4=12.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 16, we have,
\begin{array}{rcl}
C+W=16.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=40.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=32.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=72.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&72\div6\\
&=&12.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&16-12\\
&=&4.\tag{6}
\end{array}
Ava attended a American Maths Olympiad (AMO). Ava answered all 35 questions. For each correct answer, Ava will get 3 marks. However, for each wrong answer, Ava will be deducted by 1 mark(s). If Ava scored 45 marks in total, how many questions did Ava answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Ava answered all the 35 questions correctly, and each correct answer has 3 marks, then Ava should score 105 marks,
\begin{array}{rcl}
35\times3=105.
\end{array}
For every question Ava answered wrongly, Ava will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Ava only scored 45 marks, therefore Ava totally lost
\begin{array}{rcl}
105-45=60.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
60\div4=15.
\end{array}
The number of correct answers is
\begin{array}{rcl}
35-15=20.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 35, we have,
\begin{array}{rcl}
C+W=35.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=45.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=80.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&80\div4\\
&=&20.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&35-20\\
&=&15.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Ava answered all the 35 questions correctly, and each correct answer has 3 marks, then Ava should score 105 marks,
\begin{array}{rcl}
35\times3=105.
\end{array}
For every question Ava answered wrongly, Ava will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Ava only scored 45 marks, therefore Ava totally lost
\begin{array}{rcl}
105-45=60.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
60\div4=15.
\end{array}
The number of correct answers is
\begin{array}{rcl}
35-15=20.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 35, we have,
\begin{array}{rcl}
C+W=35.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=45.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=80.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&80\div4\\
&=&20.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&35-20\\
&=&15.\tag{6}
\end{array}
William attended a Australian Maths Trust (AMT). William answered all 57 questions. For each correct answer, William will get 4 marks. However, for each wrong answer, William will be deducted by 1 mark(s). If William scored 48 marks in total, how many questions did William answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume William answered all the 57 questions correctly, and each correct answer has 4 marks, then William should score 228 marks,
\begin{array}{rcl}
57\times4=228.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since William only scored 48 marks, therefore William totally lost
\begin{array}{rcl}
228-48=180.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
180\div5=36.
\end{array}
The number of correct answers is
\begin{array}{rcl}
57-36=21.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 57, we have,
\begin{array}{rcl}
C+W=57.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=48.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=105.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&105\div5\\
&=&21.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&57-21\\
&=&36.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume William answered all the 57 questions correctly, and each correct answer has 4 marks, then William should score 228 marks,
\begin{array}{rcl}
57\times4=228.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since William only scored 48 marks, therefore William totally lost
\begin{array}{rcl}
228-48=180.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
180\div5=36.
\end{array}
The number of correct answers is
\begin{array}{rcl}
57-36=21.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 57, we have,
\begin{array}{rcl}
C+W=57.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=48.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=105.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&105\div5\\
&=&21.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&57-21\\
&=&36.\tag{6}
\end{array}
Isabella attended a Australian Maths Trust (AMT). Isabella answered all 30 questions. For each correct answer, Isabella will get 4 marks. However, for each wrong answer, Isabella will be deducted by 1 mark(s). If Isabella scored 60 marks in total, how many questions did Isabella answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Isabella answered all the 30 questions correctly, and each correct answer has 4 marks, then Isabella should score 120 marks,
\begin{array}{rcl}
30\times4=120.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Isabella only scored 60 marks, therefore Isabella totally lost
\begin{array}{rcl}
120-60=60.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
60\div5=12.
\end{array}
The number of correct answers is
\begin{array}{rcl}
30-12=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 30, we have,
\begin{array}{rcl}
C+W=30.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=60.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=90.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&90\div5\\
&=&18.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&30-18\\
&=&12.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Isabella answered all the 30 questions correctly, and each correct answer has 4 marks, then Isabella should score 120 marks,
\begin{array}{rcl}
30\times4=120.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Isabella only scored 60 marks, therefore Isabella totally lost
\begin{array}{rcl}
120-60=60.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
60\div5=12.
\end{array}
The number of correct answers is
\begin{array}{rcl}
30-12=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 30, we have,
\begin{array}{rcl}
C+W=30.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=60.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=90.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&90\div5\\
&=&18.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&30-18\\
&=&12.\tag{6}
\end{array}
Liam attended a English Spelling Bee Competition. Liam answered all 20 questions. For each correct answer, Liam will get 6 marks. However, for each wrong answer, Liam will be deducted by 2 mark(s). If Liam scored 72 marks in total, how many questions did Liam answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Liam answered all the 20 questions correctly, and each correct answer has 6 marks, then Liam should score 120 marks,
\begin{array}{rcl}
20\times6=120.
\end{array}
For every question Liam answered wrongly, Liam will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Liam only scored 72 marks, therefore Liam totally lost
\begin{array}{rcl}
120-72=48.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
48\div8=6.
\end{array}
The number of correct answers is
\begin{array}{rcl}
20-6=14.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 20, we have,
\begin{array}{rcl}
C+W=20.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=72.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=40.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=112.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&112\div8\\
&=&14.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&20-14\\
&=&6.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Liam answered all the 20 questions correctly, and each correct answer has 6 marks, then Liam should score 120 marks,
\begin{array}{rcl}
20\times6=120.
\end{array}
For every question Liam answered wrongly, Liam will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Liam only scored 72 marks, therefore Liam totally lost
\begin{array}{rcl}
120-72=48.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
48\div8=6.
\end{array}
The number of correct answers is
\begin{array}{rcl}
20-6=14.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 20, we have,
\begin{array}{rcl}
C+W=20.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=72.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=40.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=112.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&112\div8\\
&=&14.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&20-14\\
&=&6.\tag{6}
\end{array}
Ava attended a American Maths Olympiad (AMO). Ava answered all 20 questions. For each correct answer, Ava will get 3 marks. However, for each wrong answer, Ava will be deducted by 1 mark(s). If Ava scored 48 marks in total, how many questions did Ava answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Ava answered all the 20 questions correctly, and each correct answer has 3 marks, then Ava should score 60 marks,
\begin{array}{rcl}
20\times3=60.
\end{array}
For every question Ava answered wrongly, Ava will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Ava only scored 48 marks, therefore Ava totally lost
\begin{array}{rcl}
60-48=12.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
12\div4=3.
\end{array}
The number of correct answers is
\begin{array}{rcl}
20-3=17.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 20, we have,
\begin{array}{rcl}
C+W=20.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=48.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=68.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&68\div4\\
&=&17.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&20-17\\
&=&3.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Ava answered all the 20 questions correctly, and each correct answer has 3 marks, then Ava should score 60 marks,
\begin{array}{rcl}
20\times3=60.
\end{array}
For every question Ava answered wrongly, Ava will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Ava only scored 48 marks, therefore Ava totally lost
\begin{array}{rcl}
60-48=12.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
12\div4=3.
\end{array}
The number of correct answers is
\begin{array}{rcl}
20-3=17.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 20, we have,
\begin{array}{rcl}
C+W=20.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=48.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=68.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&68\div4\\
&=&17.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&20-17\\
&=&3.\tag{6}
\end{array}
Mason attended a Singapore Maths Olympaid (SMO). Mason answered all 102 questions. For each correct answer, Mason will get 10 marks. However, for each wrong answer, Mason will be deducted by 2 mark(s). If Mason scored 180 marks in total, how many questions did Mason answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Mason answered all the 102 questions correctly, and each correct answer has 10 marks, then Mason should score 1020 marks,
\begin{array}{rcl}
102\times10=1020.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Mason only scored 180 marks, therefore Mason totally lost
\begin{array}{rcl}
1020-180=840.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
840\div12=70.
\end{array}
The number of correct answers is
\begin{array}{rcl}
102-70=32.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 102, we have,
\begin{array}{rcl}
C+W=102.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=180.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=204.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=384.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&384\div12\\
&=&32.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&102-32\\
&=&70.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Mason answered all the 102 questions correctly, and each correct answer has 10 marks, then Mason should score 1020 marks,
\begin{array}{rcl}
102\times10=1020.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Mason only scored 180 marks, therefore Mason totally lost
\begin{array}{rcl}
1020-180=840.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
840\div12=70.
\end{array}
The number of correct answers is
\begin{array}{rcl}
102-70=32.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 102, we have,
\begin{array}{rcl}
C+W=102.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=180.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=204.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=384.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&384\div12\\
&=&32.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&102-32\\
&=&70.\tag{6}
\end{array}
Benjamin attended a American Maths Olympiad (AMO). Benjamin answered all 72 questions. For each correct answer, Benjamin will get 10 marks. However, for each wrong answer, Benjamin will be deducted by 2 mark(s). If Benjamin scored 120 marks in total, how many questions did Benjamin answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Benjamin answered all the 72 questions correctly, and each correct answer has 10 marks, then Benjamin should score 720 marks,
\begin{array}{rcl}
72\times10=720.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Benjamin only scored 120 marks, therefore Benjamin totally lost
\begin{array}{rcl}
720-120=600.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
600\div12=50.
\end{array}
The number of correct answers is
\begin{array}{rcl}
72-50=22.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 72, we have,
\begin{array}{rcl}
C+W=72.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=120.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=144.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=264.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&264\div12\\
&=&22.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&72-22\\
&=&50.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Benjamin answered all the 72 questions correctly, and each correct answer has 10 marks, then Benjamin should score 720 marks,
\begin{array}{rcl}
72\times10=720.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Benjamin only scored 120 marks, therefore Benjamin totally lost
\begin{array}{rcl}
720-120=600.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
600\div12=50.
\end{array}
The number of correct answers is
\begin{array}{rcl}
72-50=22.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 72, we have,
\begin{array}{rcl}
C+W=72.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=120.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=144.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=264.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&264\div12\\
&=&22.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&72-22\\
&=&50.\tag{6}
\end{array}
Larry Page attended a Australian Maths Trust (AMT). Larry Page answered all 81 questions. For each correct answer, Larry Page will get 8 marks. However, for each wrong answer, Larry Page will be deducted by 2 mark(s). If Larry Page scored 88 marks in total, how many questions did Larry Page answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Larry Page answered all the 81 questions correctly, and each correct answer has 8 marks, then Larry Page should score 648 marks,
\begin{array}{rcl}
81\times8=648.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Larry Page only scored 88 marks, therefore Larry Page totally lost
\begin{array}{rcl}
648-88=560.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
560\div10=56.
\end{array}
The number of correct answers is
\begin{array}{rcl}
81-56=25.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 81, we have,
\begin{array}{rcl}
C+W=81.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=88.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=162.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=250.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&250\div10\\
&=&25.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&81-25\\
&=&56.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Larry Page answered all the 81 questions correctly, and each correct answer has 8 marks, then Larry Page should score 648 marks,
\begin{array}{rcl}
81\times8=648.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Larry Page only scored 88 marks, therefore Larry Page totally lost
\begin{array}{rcl}
648-88=560.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
560\div10=56.
\end{array}
The number of correct answers is
\begin{array}{rcl}
81-56=25.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 81, we have,
\begin{array}{rcl}
C+W=81.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=88.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=162.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=250.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&250\div10\\
&=&25.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&81-25\\
&=&56.\tag{6}
\end{array}
Ava attended a American Maths Olympiad (AMO). Ava answered all 70 questions. For each correct answer, Ava will get 5 marks. However, for each wrong answer, Ava will be deducted by 1 mark(s). If Ava scored 50 marks in total, how many questions did Ava answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Ava answered all the 70 questions correctly, and each correct answer has 5 marks, then Ava should score 350 marks,
\begin{array}{rcl}
70\times5=350.
\end{array}
For every question Ava answered wrongly, Ava will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Ava only scored 50 marks, therefore Ava totally lost
\begin{array}{rcl}
350-50=300.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
300\div6=50.
\end{array}
The number of correct answers is
\begin{array}{rcl}
70-50=20.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 70, we have,
\begin{array}{rcl}
C+W=70.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=50.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=120.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&120\div6\\
&=&20.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&70-20\\
&=&50.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Ava answered all the 70 questions correctly, and each correct answer has 5 marks, then Ava should score 350 marks,
\begin{array}{rcl}
70\times5=350.
\end{array}
For every question Ava answered wrongly, Ava will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Ava only scored 50 marks, therefore Ava totally lost
\begin{array}{rcl}
350-50=300.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
300\div6=50.
\end{array}
The number of correct answers is
\begin{array}{rcl}
70-50=20.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 70, we have,
\begin{array}{rcl}
C+W=70.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=50.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=120.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&120\div6\\
&=&20.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&70-20\\
&=&50.\tag{6}
\end{array}
James attended a Australian Maths Trust (AMT). James answered all 64 questions. For each correct answer, James will get 6 marks. However, for each wrong answer, James will be deducted by 2 mark(s). If James scored 96 marks in total, how many questions did James answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume James answered all the 64 questions correctly, and each correct answer has 6 marks, then James should score 384 marks,
\begin{array}{rcl}
64\times6=384.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since James only scored 96 marks, therefore James totally lost
\begin{array}{rcl}
384-96=288.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
288\div8=36.
\end{array}
The number of correct answers is
\begin{array}{rcl}
64-36=28.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 64, we have,
\begin{array}{rcl}
C+W=64.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=96.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=128.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=224.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&224\div8\\
&=&28.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&64-28\\
&=&36.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume James answered all the 64 questions correctly, and each correct answer has 6 marks, then James should score 384 marks,
\begin{array}{rcl}
64\times6=384.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since James only scored 96 marks, therefore James totally lost
\begin{array}{rcl}
384-96=288.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
288\div8=36.
\end{array}
The number of correct answers is
\begin{array}{rcl}
64-36=28.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 64, we have,
\begin{array}{rcl}
C+W=64.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=96.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=128.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=224.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&224\div8\\
&=&28.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&64-28\\
&=&36.\tag{6}
\end{array}
Jacob attended a Maths Competition. Jacob answered all 21 questions. For each correct answer, Jacob will get 3 marks. However, for each wrong answer, Jacob will be deducted by 1 mark(s). If Jacob scored 39 marks in total, how many questions did Jacob answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Jacob answered all the 21 questions correctly, and each correct answer has 3 marks, then Jacob should score 63 marks,
\begin{array}{rcl}
21\times3=63.
\end{array}
For every question Jacob answered wrongly, Jacob will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Jacob only scored 39 marks, therefore Jacob totally lost
\begin{array}{rcl}
63-39=24.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
24\div4=6.
\end{array}
The number of correct answers is
\begin{array}{rcl}
21-6=15.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 21, we have,
\begin{array}{rcl}
C+W=21.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=39.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=60.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&60\div4\\
&=&15.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&21-15\\
&=&6.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Jacob answered all the 21 questions correctly, and each correct answer has 3 marks, then Jacob should score 63 marks,
\begin{array}{rcl}
21\times3=63.
\end{array}
For every question Jacob answered wrongly, Jacob will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Jacob only scored 39 marks, therefore Jacob totally lost
\begin{array}{rcl}
63-39=24.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
24\div4=6.
\end{array}
The number of correct answers is
\begin{array}{rcl}
21-6=15.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 21, we have,
\begin{array}{rcl}
C+W=21.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=39.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=60.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&60\div4\\
&=&15.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&21-15\\
&=&6.\tag{6}
\end{array}
Olivia attended a Singapore Maths Olympaid (SMO). Olivia answered all 36 questions. For each correct answer, Olivia will get 6 marks. However, for each wrong answer, Olivia will be deducted by 2 mark(s). If Olivia scored 72 marks in total, how many questions did Olivia answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Olivia answered all the 36 questions correctly, and each correct answer has 6 marks, then Olivia should score 216 marks,
\begin{array}{rcl}
36\times6=216.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Olivia only scored 72 marks, therefore Olivia totally lost
\begin{array}{rcl}
216-72=144.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
144\div8=18.
\end{array}
The number of correct answers is
\begin{array}{rcl}
36-18=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 36, we have,
\begin{array}{rcl}
C+W=36.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=72.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=72.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=144.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&144\div8\\
&=&18.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&36-18\\
&=&18.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Olivia answered all the 36 questions correctly, and each correct answer has 6 marks, then Olivia should score 216 marks,
\begin{array}{rcl}
36\times6=216.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Olivia only scored 72 marks, therefore Olivia totally lost
\begin{array}{rcl}
216-72=144.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
144\div8=18.
\end{array}
The number of correct answers is
\begin{array}{rcl}
36-18=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 36, we have,
\begin{array}{rcl}
C+W=36.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=72.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=72.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=144.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&144\div8\\
&=&18.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&36-18\\
&=&18.\tag{6}
\end{array}
Mason attended a South-East Asia Maths Olympaid (SEAMO). Mason answered all 76 questions. For each correct answer, Mason will get 5 marks. However, for each wrong answer, Mason will be deducted by 1 mark(s). If Mason scored 80 marks in total, how many questions did Mason answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Mason answered all the 76 questions correctly, and each correct answer has 5 marks, then Mason should score 380 marks,
\begin{array}{rcl}
76\times5=380.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Mason only scored 80 marks, therefore Mason totally lost
\begin{array}{rcl}
380-80=300.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
300\div6=50.
\end{array}
The number of correct answers is
\begin{array}{rcl}
76-50=26.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 76, we have,
\begin{array}{rcl}
C+W=76.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=80.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=156.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&156\div6\\
&=&26.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&76-26\\
&=&50.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Mason answered all the 76 questions correctly, and each correct answer has 5 marks, then Mason should score 380 marks,
\begin{array}{rcl}
76\times5=380.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Mason only scored 80 marks, therefore Mason totally lost
\begin{array}{rcl}
380-80=300.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
300\div6=50.
\end{array}
The number of correct answers is
\begin{array}{rcl}
76-50=26.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 76, we have,
\begin{array}{rcl}
C+W=76.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=80.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=156.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&156\div6\\
&=&26.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&76-26\\
&=&50.\tag{6}
\end{array}
James attended a American Maths Olympiad (AMO). James answered all 40 questions. For each correct answer, James will get 3 marks. However, for each wrong answer, James will be deducted by 1 mark(s). If James scored 60 marks in total, how many questions did James answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume James answered all the 40 questions correctly, and each correct answer has 3 marks, then James should score 120 marks,
\begin{array}{rcl}
40\times3=120.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since James only scored 60 marks, therefore James totally lost
\begin{array}{rcl}
120-60=60.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
60\div4=15.
\end{array}
The number of correct answers is
\begin{array}{rcl}
40-15=25.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 40, we have,
\begin{array}{rcl}
C+W=40.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=60.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=100.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&100\div4\\
&=&25.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&40-25\\
&=&15.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume James answered all the 40 questions correctly, and each correct answer has 3 marks, then James should score 120 marks,
\begin{array}{rcl}
40\times3=120.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since James only scored 60 marks, therefore James totally lost
\begin{array}{rcl}
120-60=60.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
60\div4=15.
\end{array}
The number of correct answers is
\begin{array}{rcl}
40-15=25.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 40, we have,
\begin{array}{rcl}
C+W=40.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=60.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=100.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&100\div4\\
&=&25.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&40-25\\
&=&15.\tag{6}
\end{array}
Mason attended a Australian Maths Trust (AMT). Mason answered all 39 questions. For each correct answer, Mason will get 3 marks. However, for each wrong answer, Mason will be deducted by 1 mark(s). If Mason scored 33 marks in total, how many questions did Mason answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Mason answered all the 39 questions correctly, and each correct answer has 3 marks, then Mason should score 117 marks,
\begin{array}{rcl}
39\times3=117.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Mason only scored 33 marks, therefore Mason totally lost
\begin{array}{rcl}
117-33=84.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
84\div4=21.
\end{array}
The number of correct answers is
\begin{array}{rcl}
39-21=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 39, we have,
\begin{array}{rcl}
C+W=39.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=33.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=72.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&72\div4\\
&=&18.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&39-18\\
&=&21.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Mason answered all the 39 questions correctly, and each correct answer has 3 marks, then Mason should score 117 marks,
\begin{array}{rcl}
39\times3=117.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Mason only scored 33 marks, therefore Mason totally lost
\begin{array}{rcl}
117-33=84.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
84\div4=21.
\end{array}
The number of correct answers is
\begin{array}{rcl}
39-21=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 39, we have,
\begin{array}{rcl}
C+W=39.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=33.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=72.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&72\div4\\
&=&18.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&39-18\\
&=&21.\tag{6}
\end{array}
Liam attended a American Maths Olympiad (AMO). Liam answered all 12 questions. For each correct answer, Liam will get 2 marks. However, for each wrong answer, Liam will be deducted by 1 mark(s). If Liam scored 24 marks in total, how many questions did Liam answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Liam answered all the 12 questions correctly, and each correct answer has 2 marks, then Liam should score 24 marks,
\begin{array}{rcl}
12\times2=24.
\end{array}
For every question Liam answered wrongly, Liam will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Liam only scored 24 marks, therefore Liam totally lost
\begin{array}{rcl}
24-24=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div3=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
12-0=12.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 12, we have,
\begin{array}{rcl}
C+W=12.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=24.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=36.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&36\div3\\
&=&12.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&12-12\\
&=&0.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Liam answered all the 12 questions correctly, and each correct answer has 2 marks, then Liam should score 24 marks,
\begin{array}{rcl}
12\times2=24.
\end{array}
For every question Liam answered wrongly, Liam will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Liam only scored 24 marks, therefore Liam totally lost
\begin{array}{rcl}
24-24=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div3=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
12-0=12.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 12, we have,
\begin{array}{rcl}
C+W=12.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=24.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=36.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&36\div3\\
&=&12.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&12-12\\
&=&0.\tag{6}
\end{array}
William attended a American Maths Olympiad (AMO). William answered all 34 questions. For each correct answer, William will get 4 marks. However, for each wrong answer, William will be deducted by 1 mark(s). If William scored 56 marks in total, how many questions did William answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume William answered all the 34 questions correctly, and each correct answer has 4 marks, then William should score 136 marks,
\begin{array}{rcl}
34\times4=136.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since William only scored 56 marks, therefore William totally lost
\begin{array}{rcl}
136-56=80.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
80\div5=16.
\end{array}
The number of correct answers is
\begin{array}{rcl}
34-16=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 34, we have,
\begin{array}{rcl}
C+W=34.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=56.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=90.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&90\div5\\
&=&18.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&34-18\\
&=&16.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume William answered all the 34 questions correctly, and each correct answer has 4 marks, then William should score 136 marks,
\begin{array}{rcl}
34\times4=136.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since William only scored 56 marks, therefore William totally lost
\begin{array}{rcl}
136-56=80.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
80\div5=16.
\end{array}
The number of correct answers is
\begin{array}{rcl}
34-16=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 34, we have,
\begin{array}{rcl}
C+W=34.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=56.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=90.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&90\div5\\
&=&18.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&34-18\\
&=&16.\tag{6}
\end{array}
Noah attended a English Spelling Bee Competition. Noah answered all 29 questions. For each correct answer, Noah will get 2 marks. However, for each wrong answer, Noah will be deducted by 1 mark(s). If Noah scored 28 marks in total, how many questions did Noah answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Noah answered all the 29 questions correctly, and each correct answer has 2 marks, then Noah should score 58 marks,
\begin{array}{rcl}
29\times2=58.
\end{array}
For every question Noah answered wrongly, Noah will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Noah only scored 28 marks, therefore Noah totally lost
\begin{array}{rcl}
58-28=30.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
30\div3=10.
\end{array}
The number of correct answers is
\begin{array}{rcl}
29-10=19.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 29, we have,
\begin{array}{rcl}
C+W=29.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=28.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=57.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&57\div3\\
&=&19.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&29-19\\
&=&10.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Noah answered all the 29 questions correctly, and each correct answer has 2 marks, then Noah should score 58 marks,
\begin{array}{rcl}
29\times2=58.
\end{array}
For every question Noah answered wrongly, Noah will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Noah only scored 28 marks, therefore Noah totally lost
\begin{array}{rcl}
58-28=30.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
30\div3=10.
\end{array}
The number of correct answers is
\begin{array}{rcl}
29-10=19.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 29, we have,
\begin{array}{rcl}
C+W=29.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=28.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=57.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&57\div3\\
&=&19.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&29-19\\
&=&10.\tag{6}
\end{array}
Mason attended a Maths Competition. Mason answered all 40 questions. For each correct answer, Mason will get 2 marks. However, for each wrong answer, Mason will be deducted by 1 mark(s). If Mason scored 32 marks in total, how many questions did Mason answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Mason answered all the 40 questions correctly, and each correct answer has 2 marks, then Mason should score 80 marks,
\begin{array}{rcl}
40\times2=80.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Mason only scored 32 marks, therefore Mason totally lost
\begin{array}{rcl}
80-32=48.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
48\div3=16.
\end{array}
The number of correct answers is
\begin{array}{rcl}
40-16=24.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 40, we have,
\begin{array}{rcl}
C+W=40.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=32.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=72.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&72\div3\\
&=&24.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&40-24\\
&=&16.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Mason answered all the 40 questions correctly, and each correct answer has 2 marks, then Mason should score 80 marks,
\begin{array}{rcl}
40\times2=80.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Mason only scored 32 marks, therefore Mason totally lost
\begin{array}{rcl}
80-32=48.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
48\div3=16.
\end{array}
The number of correct answers is
\begin{array}{rcl}
40-16=24.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 40, we have,
\begin{array}{rcl}
C+W=40.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=32.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=72.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&72\div3\\
&=&24.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&40-24\\
&=&16.\tag{6}
\end{array}
James attended a Singapore Maths Olympaid (SMO). James answered all 98 questions. For each correct answer, James will get 6 marks. However, for each wrong answer, James will be deducted by 2 mark(s). If James scored 108 marks in total, how many questions did James answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume James answered all the 98 questions correctly, and each correct answer has 6 marks, then James should score 588 marks,
\begin{array}{rcl}
98\times6=588.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since James only scored 108 marks, therefore James totally lost
\begin{array}{rcl}
588-108=480.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
480\div8=60.
\end{array}
The number of correct answers is
\begin{array}{rcl}
98-60=38.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 98, we have,
\begin{array}{rcl}
C+W=98.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=108.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=196.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=304.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&304\div8\\
&=&38.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&98-38\\
&=&60.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume James answered all the 98 questions correctly, and each correct answer has 6 marks, then James should score 588 marks,
\begin{array}{rcl}
98\times6=588.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since James only scored 108 marks, therefore James totally lost
\begin{array}{rcl}
588-108=480.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
480\div8=60.
\end{array}
The number of correct answers is
\begin{array}{rcl}
98-60=38.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 98, we have,
\begin{array}{rcl}
C+W=98.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=108.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=196.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=304.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&304\div8\\
&=&38.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&98-38\\
&=&60.\tag{6}
\end{array}
Isabella attended a Singapore Maths Olympaid (SMO). Isabella answered all 111 questions. For each correct answer, Isabella will get 8 marks. However, for each wrong answer, Isabella will be deducted by 2 mark(s). If Isabella scored 88 marks in total, how many questions did Isabella answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Isabella answered all the 111 questions correctly, and each correct answer has 8 marks, then Isabella should score 888 marks,
\begin{array}{rcl}
111\times8=888.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Isabella only scored 88 marks, therefore Isabella totally lost
\begin{array}{rcl}
888-88=800.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
800\div10=80.
\end{array}
The number of correct answers is
\begin{array}{rcl}
111-80=31.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 111, we have,
\begin{array}{rcl}
C+W=111.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=88.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=222.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=310.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&310\div10\\
&=&31.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&111-31\\
&=&80.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Isabella answered all the 111 questions correctly, and each correct answer has 8 marks, then Isabella should score 888 marks,
\begin{array}{rcl}
111\times8=888.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Isabella only scored 88 marks, therefore Isabella totally lost
\begin{array}{rcl}
888-88=800.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
800\div10=80.
\end{array}
The number of correct answers is
\begin{array}{rcl}
111-80=31.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 111, we have,
\begin{array}{rcl}
C+W=111.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=88.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=222.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=310.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&310\div10\\
&=&31.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&111-31\\
&=&80.\tag{6}
\end{array}
Sophia attended a English Spelling Bee Competition. Sophia answered all 65 questions. For each correct answer, Sophia will get 4 marks. However, for each wrong answer, Sophia will be deducted by 1 mark(s). If Sophia scored 80 marks in total, how many questions did Sophia answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Sophia answered all the 65 questions correctly, and each correct answer has 4 marks, then Sophia should score 260 marks,
\begin{array}{rcl}
65\times4=260.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Sophia only scored 80 marks, therefore Sophia totally lost
\begin{array}{rcl}
260-80=180.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
180\div5=36.
\end{array}
The number of correct answers is
\begin{array}{rcl}
65-36=29.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 65, we have,
\begin{array}{rcl}
C+W=65.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=80.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=145.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&145\div5\\
&=&29.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&65-29\\
&=&36.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Sophia answered all the 65 questions correctly, and each correct answer has 4 marks, then Sophia should score 260 marks,
\begin{array}{rcl}
65\times4=260.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Sophia only scored 80 marks, therefore Sophia totally lost
\begin{array}{rcl}
260-80=180.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
180\div5=36.
\end{array}
The number of correct answers is
\begin{array}{rcl}
65-36=29.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 65, we have,
\begin{array}{rcl}
C+W=65.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=80.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=145.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&145\div5\\
&=&29.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&65-29\\
&=&36.\tag{6}
\end{array}
Mason attended a Australian Maths Trust (AMT). Mason answered all 22 questions. For each correct answer, Mason will get 10 marks. However, for each wrong answer, Mason will be deducted by 2 mark(s). If Mason scored 100 marks in total, how many questions did Mason answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Mason answered all the 22 questions correctly, and each correct answer has 10 marks, then Mason should score 220 marks,
\begin{array}{rcl}
22\times10=220.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Mason only scored 100 marks, therefore Mason totally lost
\begin{array}{rcl}
220-100=120.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
120\div12=10.
\end{array}
The number of correct answers is
\begin{array}{rcl}
22-10=12.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 22, we have,
\begin{array}{rcl}
C+W=22.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=100.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=44.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=144.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&144\div12\\
&=&12.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&22-12\\
&=&10.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Mason answered all the 22 questions correctly, and each correct answer has 10 marks, then Mason should score 220 marks,
\begin{array}{rcl}
22\times10=220.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Mason only scored 100 marks, therefore Mason totally lost
\begin{array}{rcl}
220-100=120.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
120\div12=10.
\end{array}
The number of correct answers is
\begin{array}{rcl}
22-10=12.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 22, we have,
\begin{array}{rcl}
C+W=22.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=100.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=44.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=144.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&144\div12\\
&=&12.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&22-12\\
&=&10.\tag{6}
\end{array}
Emma attended a South-East Asia Maths Olympaid (SEAMO). Emma answered all 48 questions. For each correct answer, Emma will get 4 marks. However, for each wrong answer, Emma will be deducted by 2 mark(s). If Emma scored 72 marks in total, how many questions did Emma answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Emma answered all the 48 questions correctly, and each correct answer has 4 marks, then Emma should score 192 marks,
\begin{array}{rcl}
48\times4=192.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Emma only scored 72 marks, therefore Emma totally lost
\begin{array}{rcl}
192-72=120.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
120\div6=20.
\end{array}
The number of correct answers is
\begin{array}{rcl}
48-20=28.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 48, we have,
\begin{array}{rcl}
C+W=48.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=72.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=96.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=168.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&168\div6\\
&=&28.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&48-28\\
&=&20.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Emma answered all the 48 questions correctly, and each correct answer has 4 marks, then Emma should score 192 marks,
\begin{array}{rcl}
48\times4=192.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Emma only scored 72 marks, therefore Emma totally lost
\begin{array}{rcl}
192-72=120.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
120\div6=20.
\end{array}
The number of correct answers is
\begin{array}{rcl}
48-20=28.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 48, we have,
\begin{array}{rcl}
C+W=48.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=72.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=96.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=168.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&168\div6\\
&=&28.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&48-28\\
&=&20.\tag{6}
\end{array}
Benjamin attended a Maths Competition. Benjamin answered all 74 questions. For each correct answer, Benjamin will get 4 marks. However, for each wrong answer, Benjamin will be deducted by 2 mark(s). If Benjamin scored 56 marks in total, how many questions did Benjamin answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Benjamin answered all the 74 questions correctly, and each correct answer has 4 marks, then Benjamin should score 296 marks,
\begin{array}{rcl}
74\times4=296.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Benjamin only scored 56 marks, therefore Benjamin totally lost
\begin{array}{rcl}
296-56=240.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
240\div6=40.
\end{array}
The number of correct answers is
\begin{array}{rcl}
74-40=34.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 74, we have,
\begin{array}{rcl}
C+W=74.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=56.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=148.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=204.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&204\div6\\
&=&34.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&74-34\\
&=&40.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Benjamin answered all the 74 questions correctly, and each correct answer has 4 marks, then Benjamin should score 296 marks,
\begin{array}{rcl}
74\times4=296.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Benjamin only scored 56 marks, therefore Benjamin totally lost
\begin{array}{rcl}
296-56=240.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
240\div6=40.
\end{array}
The number of correct answers is
\begin{array}{rcl}
74-40=34.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 74, we have,
\begin{array}{rcl}
C+W=74.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=56.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=148.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=204.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&204\div6\\
&=&34.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&74-34\\
&=&40.\tag{6}
\end{array}
Ava attended a Chinese Multiple Choices Test. Ava answered all 138 questions. For each correct answer, Ava will get 10 marks. However, for each wrong answer, Ava will be deducted by 2 mark(s). If Ava scored 180 marks in total, how many questions did Ava answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Ava answered all the 138 questions correctly, and each correct answer has 10 marks, then Ava should score 1380 marks,
\begin{array}{rcl}
138\times10=1380.
\end{array}
For every question Ava answered wrongly, Ava will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Ava only scored 180 marks, therefore Ava totally lost
\begin{array}{rcl}
1380-180=1200.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
1200\div12=100.
\end{array}
The number of correct answers is
\begin{array}{rcl}
138-100=38.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 138, we have,
\begin{array}{rcl}
C+W=138.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=180.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=276.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=456.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&456\div12\\
&=&38.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&138-38\\
&=&100.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Ava answered all the 138 questions correctly, and each correct answer has 10 marks, then Ava should score 1380 marks,
\begin{array}{rcl}
138\times10=1380.
\end{array}
For every question Ava answered wrongly, Ava will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Ava only scored 180 marks, therefore Ava totally lost
\begin{array}{rcl}
1380-180=1200.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
1200\div12=100.
\end{array}
The number of correct answers is
\begin{array}{rcl}
138-100=38.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 138, we have,
\begin{array}{rcl}
C+W=138.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=180.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=276.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=456.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&456\div12\\
&=&38.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&138-38\\
&=&100.\tag{6}
\end{array}
Larry Page attended a Australian Maths Trust (AMT). Larry Page answered all 72 questions. For each correct answer, Larry Page will get 8 marks. However, for each wrong answer, Larry Page will be deducted by 2 mark(s). If Larry Page scored 96 marks in total, how many questions did Larry Page answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Larry Page answered all the 72 questions correctly, and each correct answer has 8 marks, then Larry Page should score 576 marks,
\begin{array}{rcl}
72\times8=576.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Larry Page only scored 96 marks, therefore Larry Page totally lost
\begin{array}{rcl}
576-96=480.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
480\div10=48.
\end{array}
The number of correct answers is
\begin{array}{rcl}
72-48=24.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 72, we have,
\begin{array}{rcl}
C+W=72.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=96.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=144.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=240.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&240\div10\\
&=&24.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&72-24\\
&=&48.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Larry Page answered all the 72 questions correctly, and each correct answer has 8 marks, then Larry Page should score 576 marks,
\begin{array}{rcl}
72\times8=576.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Larry Page only scored 96 marks, therefore Larry Page totally lost
\begin{array}{rcl}
576-96=480.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
480\div10=48.
\end{array}
The number of correct answers is
\begin{array}{rcl}
72-48=24.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 72, we have,
\begin{array}{rcl}
C+W=72.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=96.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=144.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=240.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&240\div10\\
&=&24.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&72-24\\
&=&48.\tag{6}
\end{array}
Mason attended a Maths Competition. Mason answered all 92 questions. For each correct answer, Mason will get 6 marks. However, for each wrong answer, Mason will be deducted by 2 mark(s). If Mason scored 72 marks in total, how many questions did Mason answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Mason answered all the 92 questions correctly, and each correct answer has 6 marks, then Mason should score 552 marks,
\begin{array}{rcl}
92\times6=552.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Mason only scored 72 marks, therefore Mason totally lost
\begin{array}{rcl}
552-72=480.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
480\div8=60.
\end{array}
The number of correct answers is
\begin{array}{rcl}
92-60=32.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 92, we have,
\begin{array}{rcl}
C+W=92.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=72.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=184.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=256.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&256\div8\\
&=&32.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&92-32\\
&=&60.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Mason answered all the 92 questions correctly, and each correct answer has 6 marks, then Mason should score 552 marks,
\begin{array}{rcl}
92\times6=552.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Mason only scored 72 marks, therefore Mason totally lost
\begin{array}{rcl}
552-72=480.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
480\div8=60.
\end{array}
The number of correct answers is
\begin{array}{rcl}
92-60=32.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 92, we have,
\begin{array}{rcl}
C+W=92.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=72.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=184.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=256.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&256\div8\\
&=&32.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&92-32\\
&=&60.\tag{6}
\end{array}
Jacob attended a Australian Maths Trust (AMT). Jacob answered all 53 questions. For each correct answer, Jacob will get 4 marks. However, for each wrong answer, Jacob will be deducted by 1 mark(s). If Jacob scored 72 marks in total, how many questions did Jacob answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Jacob answered all the 53 questions correctly, and each correct answer has 4 marks, then Jacob should score 212 marks,
\begin{array}{rcl}
53\times4=212.
\end{array}
For every question Jacob answered wrongly, Jacob will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Jacob only scored 72 marks, therefore Jacob totally lost
\begin{array}{rcl}
212-72=140.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
140\div5=28.
\end{array}
The number of correct answers is
\begin{array}{rcl}
53-28=25.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 53, we have,
\begin{array}{rcl}
C+W=53.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=72.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=125.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&125\div5\\
&=&25.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&53-25\\
&=&28.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Jacob answered all the 53 questions correctly, and each correct answer has 4 marks, then Jacob should score 212 marks,
\begin{array}{rcl}
53\times4=212.
\end{array}
For every question Jacob answered wrongly, Jacob will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Jacob only scored 72 marks, therefore Jacob totally lost
\begin{array}{rcl}
212-72=140.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
140\div5=28.
\end{array}
The number of correct answers is
\begin{array}{rcl}
53-28=25.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 53, we have,
\begin{array}{rcl}
C+W=53.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=72.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=125.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&125\div5\\
&=&25.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&53-25\\
&=&28.\tag{6}
\end{array}
Sophia attended a Chinese Multiple Choices Test. Sophia answered all 96 questions. For each correct answer, Sophia will get 6 marks. However, for each wrong answer, Sophia will be deducted by 2 mark(s). If Sophia scored 96 marks in total, how many questions did Sophia answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Sophia answered all the 96 questions correctly, and each correct answer has 6 marks, then Sophia should score 576 marks,
\begin{array}{rcl}
96\times6=576.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Sophia only scored 96 marks, therefore Sophia totally lost
\begin{array}{rcl}
576-96=480.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
480\div8=60.
\end{array}
The number of correct answers is
\begin{array}{rcl}
96-60=36.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 96, we have,
\begin{array}{rcl}
C+W=96.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=96.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=192.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=288.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&288\div8\\
&=&36.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&96-36\\
&=&60.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Sophia answered all the 96 questions correctly, and each correct answer has 6 marks, then Sophia should score 576 marks,
\begin{array}{rcl}
96\times6=576.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Sophia only scored 96 marks, therefore Sophia totally lost
\begin{array}{rcl}
576-96=480.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
480\div8=60.
\end{array}
The number of correct answers is
\begin{array}{rcl}
96-60=36.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 96, we have,
\begin{array}{rcl}
C+W=96.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=96.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=192.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=288.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&288\div8\\
&=&36.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&96-36\\
&=&60.\tag{6}
\end{array}
Ava attended a Australian Maths Trust (AMT). Ava answered all 57 questions. For each correct answer, Ava will get 4 marks. However, for each wrong answer, Ava will be deducted by 2 mark(s). If Ava scored 60 marks in total, how many questions did Ava answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Ava answered all the 57 questions correctly, and each correct answer has 4 marks, then Ava should score 228 marks,
\begin{array}{rcl}
57\times4=228.
\end{array}
For every question Ava answered wrongly, Ava will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Ava only scored 60 marks, therefore Ava totally lost
\begin{array}{rcl}
228-60=168.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
168\div6=28.
\end{array}
The number of correct answers is
\begin{array}{rcl}
57-28=29.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 57, we have,
\begin{array}{rcl}
C+W=57.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=60.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=114.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=174.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&174\div6\\
&=&29.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&57-29\\
&=&28.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Ava answered all the 57 questions correctly, and each correct answer has 4 marks, then Ava should score 228 marks,
\begin{array}{rcl}
57\times4=228.
\end{array}
For every question Ava answered wrongly, Ava will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Ava only scored 60 marks, therefore Ava totally lost
\begin{array}{rcl}
228-60=168.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
168\div6=28.
\end{array}
The number of correct answers is
\begin{array}{rcl}
57-28=29.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 57, we have,
\begin{array}{rcl}
C+W=57.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=60.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=114.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=174.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&174\div6\\
&=&29.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&57-29\\
&=&28.\tag{6}
\end{array}
Larry Page attended a Australian Maths Trust (AMT). Larry Page answered all 36 questions. For each correct answer, Larry Page will get 2 marks. However, for each wrong answer, Larry Page will be deducted by 1 mark(s). If Larry Page scored 36 marks in total, how many questions did Larry Page answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Larry Page answered all the 36 questions correctly, and each correct answer has 2 marks, then Larry Page should score 72 marks,
\begin{array}{rcl}
36\times2=72.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Larry Page only scored 36 marks, therefore Larry Page totally lost
\begin{array}{rcl}
72-36=36.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
36\div3=12.
\end{array}
The number of correct answers is
\begin{array}{rcl}
36-12=24.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 36, we have,
\begin{array}{rcl}
C+W=36.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=36.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=72.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&72\div3\\
&=&24.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&36-24\\
&=&12.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Larry Page answered all the 36 questions correctly, and each correct answer has 2 marks, then Larry Page should score 72 marks,
\begin{array}{rcl}
36\times2=72.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Larry Page only scored 36 marks, therefore Larry Page totally lost
\begin{array}{rcl}
72-36=36.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
36\div3=12.
\end{array}
The number of correct answers is
\begin{array}{rcl}
36-12=24.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 36, we have,
\begin{array}{rcl}
C+W=36.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=36.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=72.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&72\div3\\
&=&24.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&36-24\\
&=&12.\tag{6}
\end{array}
Liam attended a Maths Competition. Liam answered all 40 questions. For each correct answer, Liam will get 2 marks. However, for each wrong answer, Liam will be deducted by 1 mark(s). If Liam scored 38 marks in total, how many questions did Liam answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Liam answered all the 40 questions correctly, and each correct answer has 2 marks, then Liam should score 80 marks,
\begin{array}{rcl}
40\times2=80.
\end{array}
For every question Liam answered wrongly, Liam will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Liam only scored 38 marks, therefore Liam totally lost
\begin{array}{rcl}
80-38=42.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
42\div3=14.
\end{array}
The number of correct answers is
\begin{array}{rcl}
40-14=26.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 40, we have,
\begin{array}{rcl}
C+W=40.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=38.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=78.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&78\div3\\
&=&26.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&40-26\\
&=&14.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Liam answered all the 40 questions correctly, and each correct answer has 2 marks, then Liam should score 80 marks,
\begin{array}{rcl}
40\times2=80.
\end{array}
For every question Liam answered wrongly, Liam will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Liam only scored 38 marks, therefore Liam totally lost
\begin{array}{rcl}
80-38=42.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
42\div3=14.
\end{array}
The number of correct answers is
\begin{array}{rcl}
40-14=26.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 40, we have,
\begin{array}{rcl}
C+W=40.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=38.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=78.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&78\div3\\
&=&26.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&40-26\\
&=&14.\tag{6}
\end{array}
Noah attended a Australian Maths Trust (AMT). Noah answered all 37 questions. For each correct answer, Noah will get 4 marks. However, for each wrong answer, Noah will be deducted by 1 mark(s). If Noah scored 68 marks in total, how many questions did Noah answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Noah answered all the 37 questions correctly, and each correct answer has 4 marks, then Noah should score 148 marks,
\begin{array}{rcl}
37\times4=148.
\end{array}
For every question Noah answered wrongly, Noah will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Noah only scored 68 marks, therefore Noah totally lost
\begin{array}{rcl}
148-68=80.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
80\div5=16.
\end{array}
The number of correct answers is
\begin{array}{rcl}
37-16=21.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 37, we have,
\begin{array}{rcl}
C+W=37.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=68.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=105.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&105\div5\\
&=&21.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&37-21\\
&=&16.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Noah answered all the 37 questions correctly, and each correct answer has 4 marks, then Noah should score 148 marks,
\begin{array}{rcl}
37\times4=148.
\end{array}
For every question Noah answered wrongly, Noah will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Noah only scored 68 marks, therefore Noah totally lost
\begin{array}{rcl}
148-68=80.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
80\div5=16.
\end{array}
The number of correct answers is
\begin{array}{rcl}
37-16=21.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 37, we have,
\begin{array}{rcl}
C+W=37.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=68.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=105.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&105\div5\\
&=&21.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&37-21\\
&=&16.\tag{6}
\end{array}
Larry Page attended a Chinese Multiple Choices Test. Larry Page answered all 59 questions. For each correct answer, Larry Page will get 4 marks. However, for each wrong answer, Larry Page will be deducted by 2 mark(s). If Larry Page scored 44 marks in total, how many questions did Larry Page answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Larry Page answered all the 59 questions correctly, and each correct answer has 4 marks, then Larry Page should score 236 marks,
\begin{array}{rcl}
59\times4=236.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Larry Page only scored 44 marks, therefore Larry Page totally lost
\begin{array}{rcl}
236-44=192.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
192\div6=32.
\end{array}
The number of correct answers is
\begin{array}{rcl}
59-32=27.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 59, we have,
\begin{array}{rcl}
C+W=59.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=44.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=118.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=162.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&162\div6\\
&=&27.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&59-27\\
&=&32.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Larry Page answered all the 59 questions correctly, and each correct answer has 4 marks, then Larry Page should score 236 marks,
\begin{array}{rcl}
59\times4=236.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Larry Page only scored 44 marks, therefore Larry Page totally lost
\begin{array}{rcl}
236-44=192.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
192\div6=32.
\end{array}
The number of correct answers is
\begin{array}{rcl}
59-32=27.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 59, we have,
\begin{array}{rcl}
C+W=59.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=44.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=118.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=162.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&162\div6\\
&=&27.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&59-27\\
&=&32.\tag{6}
\end{array}
Emma attended a Maths Competition. Emma answered all 60 questions. For each correct answer, Emma will get 4 marks. However, for each wrong answer, Emma will be deducted by 1 mark(s). If Emma scored 80 marks in total, how many questions did Emma answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Emma answered all the 60 questions correctly, and each correct answer has 4 marks, then Emma should score 240 marks,
\begin{array}{rcl}
60\times4=240.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Emma only scored 80 marks, therefore Emma totally lost
\begin{array}{rcl}
240-80=160.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
160\div5=32.
\end{array}
The number of correct answers is
\begin{array}{rcl}
60-32=28.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 60, we have,
\begin{array}{rcl}
C+W=60.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=80.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=140.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&140\div5\\
&=&28.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&60-28\\
&=&32.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Emma answered all the 60 questions correctly, and each correct answer has 4 marks, then Emma should score 240 marks,
\begin{array}{rcl}
60\times4=240.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Emma only scored 80 marks, therefore Emma totally lost
\begin{array}{rcl}
240-80=160.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
160\div5=32.
\end{array}
The number of correct answers is
\begin{array}{rcl}
60-32=28.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 60, we have,
\begin{array}{rcl}
C+W=60.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=80.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=140.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&140\div5\\
&=&28.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&60-28\\
&=&32.\tag{6}
\end{array}
Olivia attended a Chinese Multiple Choices Test. Olivia answered all 28 questions. For each correct answer, Olivia will get 10 marks. However, for each wrong answer, Olivia will be deducted by 2 mark(s). If Olivia scored 160 marks in total, how many questions did Olivia answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Olivia answered all the 28 questions correctly, and each correct answer has 10 marks, then Olivia should score 280 marks,
\begin{array}{rcl}
28\times10=280.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Olivia only scored 160 marks, therefore Olivia totally lost
\begin{array}{rcl}
280-160=120.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
120\div12=10.
\end{array}
The number of correct answers is
\begin{array}{rcl}
28-10=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 28, we have,
\begin{array}{rcl}
C+W=28.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=160.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=56.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=216.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&216\div12\\
&=&18.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&28-18\\
&=&10.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Olivia answered all the 28 questions correctly, and each correct answer has 10 marks, then Olivia should score 280 marks,
\begin{array}{rcl}
28\times10=280.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Olivia only scored 160 marks, therefore Olivia totally lost
\begin{array}{rcl}
280-160=120.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
120\div12=10.
\end{array}
The number of correct answers is
\begin{array}{rcl}
28-10=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 28, we have,
\begin{array}{rcl}
C+W=28.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=160.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=56.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=216.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&216\div12\\
&=&18.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&28-18\\
&=&10.\tag{6}
\end{array}
William attended a Maths Competition. William answered all 32 questions. For each correct answer, William will get 8 marks. However, for each wrong answer, William will be deducted by 2 mark(s). If William scored 96 marks in total, how many questions did William answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume William answered all the 32 questions correctly, and each correct answer has 8 marks, then William should score 256 marks,
\begin{array}{rcl}
32\times8=256.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since William only scored 96 marks, therefore William totally lost
\begin{array}{rcl}
256-96=160.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
160\div10=16.
\end{array}
The number of correct answers is
\begin{array}{rcl}
32-16=16.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 32, we have,
\begin{array}{rcl}
C+W=32.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=96.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=64.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=160.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&160\div10\\
&=&16.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&32-16\\
&=&16.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume William answered all the 32 questions correctly, and each correct answer has 8 marks, then William should score 256 marks,
\begin{array}{rcl}
32\times8=256.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since William only scored 96 marks, therefore William totally lost
\begin{array}{rcl}
256-96=160.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
160\div10=16.
\end{array}
The number of correct answers is
\begin{array}{rcl}
32-16=16.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 32, we have,
\begin{array}{rcl}
C+W=32.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=96.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=64.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=160.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&160\div10\\
&=&16.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&32-16\\
&=&16.\tag{6}
\end{array}
William attended a Chinese Multiple Choices Test. William answered all 86 questions. For each correct answer, William will get 6 marks. However, for each wrong answer, William will be deducted by 2 mark(s). If William scored 84 marks in total, how many questions did William answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume William answered all the 86 questions correctly, and each correct answer has 6 marks, then William should score 516 marks,
\begin{array}{rcl}
86\times6=516.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since William only scored 84 marks, therefore William totally lost
\begin{array}{rcl}
516-84=432.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
432\div8=54.
\end{array}
The number of correct answers is
\begin{array}{rcl}
86-54=32.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 86, we have,
\begin{array}{rcl}
C+W=86.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=84.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=172.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=256.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&256\div8\\
&=&32.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&86-32\\
&=&54.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume William answered all the 86 questions correctly, and each correct answer has 6 marks, then William should score 516 marks,
\begin{array}{rcl}
86\times6=516.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since William only scored 84 marks, therefore William totally lost
\begin{array}{rcl}
516-84=432.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
432\div8=54.
\end{array}
The number of correct answers is
\begin{array}{rcl}
86-54=32.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 86, we have,
\begin{array}{rcl}
C+W=86.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=84.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=172.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=256.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&256\div8\\
&=&32.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&86-32\\
&=&54.\tag{6}
\end{array}
Jacob attended a Singapore Maths Olympaid (SMO). Jacob answered all 56 questions. For each correct answer, Jacob will get 3 marks. However, for each wrong answer, Jacob will be deducted by 1 mark(s). If Jacob scored 48 marks in total, how many questions did Jacob answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Jacob answered all the 56 questions correctly, and each correct answer has 3 marks, then Jacob should score 168 marks,
\begin{array}{rcl}
56\times3=168.
\end{array}
For every question Jacob answered wrongly, Jacob will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Jacob only scored 48 marks, therefore Jacob totally lost
\begin{array}{rcl}
168-48=120.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
120\div4=30.
\end{array}
The number of correct answers is
\begin{array}{rcl}
56-30=26.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 56, we have,
\begin{array}{rcl}
C+W=56.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=48.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=104.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&104\div4\\
&=&26.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&56-26\\
&=&30.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Jacob answered all the 56 questions correctly, and each correct answer has 3 marks, then Jacob should score 168 marks,
\begin{array}{rcl}
56\times3=168.
\end{array}
For every question Jacob answered wrongly, Jacob will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Jacob only scored 48 marks, therefore Jacob totally lost
\begin{array}{rcl}
168-48=120.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
120\div4=30.
\end{array}
The number of correct answers is
\begin{array}{rcl}
56-30=26.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 56, we have,
\begin{array}{rcl}
C+W=56.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=48.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=104.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&104\div4\\
&=&26.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&56-26\\
&=&30.\tag{6}
\end{array}
Benjamin attended a American Maths Olympiad (AMO). Benjamin answered all 118 questions. For each correct answer, Benjamin will get 10 marks. However, for each wrong answer, Benjamin will be deducted by 2 mark(s). If Benjamin scored 100 marks in total, how many questions did Benjamin answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Benjamin answered all the 118 questions correctly, and each correct answer has 10 marks, then Benjamin should score 1180 marks,
\begin{array}{rcl}
118\times10=1180.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Benjamin only scored 100 marks, therefore Benjamin totally lost
\begin{array}{rcl}
1180-100=1080.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
1080\div12=90.
\end{array}
The number of correct answers is
\begin{array}{rcl}
118-90=28.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 118, we have,
\begin{array}{rcl}
C+W=118.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=100.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=236.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=336.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&336\div12\\
&=&28.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&118-28\\
&=&90.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Benjamin answered all the 118 questions correctly, and each correct answer has 10 marks, then Benjamin should score 1180 marks,
\begin{array}{rcl}
118\times10=1180.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Benjamin only scored 100 marks, therefore Benjamin totally lost
\begin{array}{rcl}
1180-100=1080.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
1080\div12=90.
\end{array}
The number of correct answers is
\begin{array}{rcl}
118-90=28.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 118, we have,
\begin{array}{rcl}
C+W=118.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=100.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=236.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=336.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&336\div12\\
&=&28.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&118-28\\
&=&90.\tag{6}
\end{array}
Bill Gates attended a South-East Asia Maths Olympaid (SEAMO). Bill Gates answered all 17 questions. For each correct answer, Bill Gates will get 4 marks. However, for each wrong answer, Bill Gates will be deducted by 1 mark(s). If Bill Gates scored 48 marks in total, how many questions did Bill Gates answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Bill Gates answered all the 17 questions correctly, and each correct answer has 4 marks, then Bill Gates should score 68 marks,
\begin{array}{rcl}
17\times4=68.
\end{array}
For every question Bill Gates answered wrongly, Bill Gates will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Bill Gates only scored 48 marks, therefore Bill Gates totally lost
\begin{array}{rcl}
68-48=20.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
20\div5=4.
\end{array}
The number of correct answers is
\begin{array}{rcl}
17-4=13.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 17, we have,
\begin{array}{rcl}
C+W=17.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=48.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=65.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&65\div5\\
&=&13.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&17-13\\
&=&4.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Bill Gates answered all the 17 questions correctly, and each correct answer has 4 marks, then Bill Gates should score 68 marks,
\begin{array}{rcl}
17\times4=68.
\end{array}
For every question Bill Gates answered wrongly, Bill Gates will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Bill Gates only scored 48 marks, therefore Bill Gates totally lost
\begin{array}{rcl}
68-48=20.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
20\div5=4.
\end{array}
The number of correct answers is
\begin{array}{rcl}
17-4=13.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 17, we have,
\begin{array}{rcl}
C+W=17.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=48.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=65.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&65\div5\\
&=&13.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&17-13\\
&=&4.\tag{6}
\end{array}
Jacob attended a Australian Maths Trust (AMT). Jacob answered all 40 questions. For each correct answer, Jacob will get 3 marks. However, for each wrong answer, Jacob will be deducted by 1 mark(s). If Jacob scored 48 marks in total, how many questions did Jacob answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Jacob answered all the 40 questions correctly, and each correct answer has 3 marks, then Jacob should score 120 marks,
\begin{array}{rcl}
40\times3=120.
\end{array}
For every question Jacob answered wrongly, Jacob will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Jacob only scored 48 marks, therefore Jacob totally lost
\begin{array}{rcl}
120-48=72.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
72\div4=18.
\end{array}
The number of correct answers is
\begin{array}{rcl}
40-18=22.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 40, we have,
\begin{array}{rcl}
C+W=40.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=48.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=88.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&88\div4\\
&=&22.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&40-22\\
&=&18.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Jacob answered all the 40 questions correctly, and each correct answer has 3 marks, then Jacob should score 120 marks,
\begin{array}{rcl}
40\times3=120.
\end{array}
For every question Jacob answered wrongly, Jacob will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Jacob only scored 48 marks, therefore Jacob totally lost
\begin{array}{rcl}
120-48=72.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
72\div4=18.
\end{array}
The number of correct answers is
\begin{array}{rcl}
40-18=22.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 40, we have,
\begin{array}{rcl}
C+W=40.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=48.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=88.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&88\div4\\
&=&22.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&40-22\\
&=&18.\tag{6}
\end{array}
Olivia attended a Australian Maths Trust (AMT). Olivia answered all 13 questions. For each correct answer, Olivia will get 4 marks. However, for each wrong answer, Olivia will be deducted by 1 mark(s). If Olivia scored 52 marks in total, how many questions did Olivia answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Olivia answered all the 13 questions correctly, and each correct answer has 4 marks, then Olivia should score 52 marks,
\begin{array}{rcl}
13\times4=52.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Olivia only scored 52 marks, therefore Olivia totally lost
\begin{array}{rcl}
52-52=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div5=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
13-0=13.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 13, we have,
\begin{array}{rcl}
C+W=13.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=52.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=65.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&65\div5\\
&=&13.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&13-13\\
&=&0.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Olivia answered all the 13 questions correctly, and each correct answer has 4 marks, then Olivia should score 52 marks,
\begin{array}{rcl}
13\times4=52.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Olivia only scored 52 marks, therefore Olivia totally lost
\begin{array}{rcl}
52-52=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div5=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
13-0=13.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 13, we have,
\begin{array}{rcl}
C+W=13.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=52.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=65.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&65\div5\\
&=&13.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&13-13\\
&=&0.\tag{6}
\end{array}
Emma attended a Chinese Multiple Choices Test. Emma answered all 49 questions. For each correct answer, Emma will get 4 marks. However, for each wrong answer, Emma will be deducted by 2 mark(s). If Emma scored 52 marks in total, how many questions did Emma answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Emma answered all the 49 questions correctly, and each correct answer has 4 marks, then Emma should score 196 marks,
\begin{array}{rcl}
49\times4=196.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Emma only scored 52 marks, therefore Emma totally lost
\begin{array}{rcl}
196-52=144.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
144\div6=24.
\end{array}
The number of correct answers is
\begin{array}{rcl}
49-24=25.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 49, we have,
\begin{array}{rcl}
C+W=49.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=52.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=98.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=150.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&150\div6\\
&=&25.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&49-25\\
&=&24.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Emma answered all the 49 questions correctly, and each correct answer has 4 marks, then Emma should score 196 marks,
\begin{array}{rcl}
49\times4=196.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Emma only scored 52 marks, therefore Emma totally lost
\begin{array}{rcl}
196-52=144.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
144\div6=24.
\end{array}
The number of correct answers is
\begin{array}{rcl}
49-24=25.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 49, we have,
\begin{array}{rcl}
C+W=49.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=52.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=98.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=150.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&150\div6\\
&=&25.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&49-25\\
&=&24.\tag{6}
\end{array}
James attended a Chinese Multiple Choices Test. James answered all 77 questions. For each correct answer, James will get 4 marks. However, for each wrong answer, James will be deducted by 2 mark(s). If James scored 68 marks in total, how many questions did James answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume James answered all the 77 questions correctly, and each correct answer has 4 marks, then James should score 308 marks,
\begin{array}{rcl}
77\times4=308.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since James only scored 68 marks, therefore James totally lost
\begin{array}{rcl}
308-68=240.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
240\div6=40.
\end{array}
The number of correct answers is
\begin{array}{rcl}
77-40=37.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 77, we have,
\begin{array}{rcl}
C+W=77.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=68.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=154.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=222.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&222\div6\\
&=&37.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&77-37\\
&=&40.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume James answered all the 77 questions correctly, and each correct answer has 4 marks, then James should score 308 marks,
\begin{array}{rcl}
77\times4=308.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since James only scored 68 marks, therefore James totally lost
\begin{array}{rcl}
308-68=240.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
240\div6=40.
\end{array}
The number of correct answers is
\begin{array}{rcl}
77-40=37.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 77, we have,
\begin{array}{rcl}
C+W=77.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=68.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=154.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=222.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&222\div6\\
&=&37.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&77-37\\
&=&40.\tag{6}
\end{array}
Liam attended a American Maths Olympiad (AMO). Liam answered all 38 questions. For each correct answer, Liam will get 4 marks. However, for each wrong answer, Liam will be deducted by 2 mark(s). If Liam scored 80 marks in total, how many questions did Liam answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Liam answered all the 38 questions correctly, and each correct answer has 4 marks, then Liam should score 152 marks,
\begin{array}{rcl}
38\times4=152.
\end{array}
For every question Liam answered wrongly, Liam will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Liam only scored 80 marks, therefore Liam totally lost
\begin{array}{rcl}
152-80=72.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
72\div6=12.
\end{array}
The number of correct answers is
\begin{array}{rcl}
38-12=26.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 38, we have,
\begin{array}{rcl}
C+W=38.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=80.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=76.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=156.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&156\div6\\
&=&26.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&38-26\\
&=&12.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Liam answered all the 38 questions correctly, and each correct answer has 4 marks, then Liam should score 152 marks,
\begin{array}{rcl}
38\times4=152.
\end{array}
For every question Liam answered wrongly, Liam will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Liam only scored 80 marks, therefore Liam totally lost
\begin{array}{rcl}
152-80=72.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
72\div6=12.
\end{array}
The number of correct answers is
\begin{array}{rcl}
38-12=26.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 38, we have,
\begin{array}{rcl}
C+W=38.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=80.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=76.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=156.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&156\div6\\
&=&26.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&38-26\\
&=&12.\tag{6}
\end{array}
Ava attended a Australian Maths Trust (AMT). Ava answered all 20 questions. For each correct answer, Ava will get 6 marks. However, for each wrong answer, Ava will be deducted by 2 mark(s). If Ava scored 120 marks in total, how many questions did Ava answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Ava answered all the 20 questions correctly, and each correct answer has 6 marks, then Ava should score 120 marks,
\begin{array}{rcl}
20\times6=120.
\end{array}
For every question Ava answered wrongly, Ava will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Ava only scored 120 marks, therefore Ava totally lost
\begin{array}{rcl}
120-120=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div8=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
20-0=20.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 20, we have,
\begin{array}{rcl}
C+W=20.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=120.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=40.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=160.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&160\div8\\
&=&20.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&20-20\\
&=&0.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Ava answered all the 20 questions correctly, and each correct answer has 6 marks, then Ava should score 120 marks,
\begin{array}{rcl}
20\times6=120.
\end{array}
For every question Ava answered wrongly, Ava will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Ava only scored 120 marks, therefore Ava totally lost
\begin{array}{rcl}
120-120=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div8=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
20-0=20.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 20, we have,
\begin{array}{rcl}
C+W=20.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=120.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=40.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=160.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&160\div8\\
&=&20.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&20-20\\
&=&0.\tag{6}
\end{array}
Benjamin attended a English Spelling Bee Competition. Benjamin answered all 71 questions. For each correct answer, Benjamin will get 6 marks. However, for each wrong answer, Benjamin will be deducted by 2 mark(s). If Benjamin scored 90 marks in total, how many questions did Benjamin answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Benjamin answered all the 71 questions correctly, and each correct answer has 6 marks, then Benjamin should score 426 marks,
\begin{array}{rcl}
71\times6=426.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Benjamin only scored 90 marks, therefore Benjamin totally lost
\begin{array}{rcl}
426-90=336.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
336\div8=42.
\end{array}
The number of correct answers is
\begin{array}{rcl}
71-42=29.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 71, we have,
\begin{array}{rcl}
C+W=71.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=90.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=142.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=232.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&232\div8\\
&=&29.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&71-29\\
&=&42.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Benjamin answered all the 71 questions correctly, and each correct answer has 6 marks, then Benjamin should score 426 marks,
\begin{array}{rcl}
71\times6=426.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Benjamin only scored 90 marks, therefore Benjamin totally lost
\begin{array}{rcl}
426-90=336.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
336\div8=42.
\end{array}
The number of correct answers is
\begin{array}{rcl}
71-42=29.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 71, we have,
\begin{array}{rcl}
C+W=71.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=90.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=142.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=232.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&232\div8\\
&=&29.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&71-29\\
&=&42.\tag{6}
\end{array}
William attended a American Maths Olympiad (AMO). William answered all 51 questions. For each correct answer, William will get 4 marks. However, for each wrong answer, William will be deducted by 2 mark(s). If William scored 60 marks in total, how many questions did William answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume William answered all the 51 questions correctly, and each correct answer has 4 marks, then William should score 204 marks,
\begin{array}{rcl}
51\times4=204.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since William only scored 60 marks, therefore William totally lost
\begin{array}{rcl}
204-60=144.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
144\div6=24.
\end{array}
The number of correct answers is
\begin{array}{rcl}
51-24=27.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 51, we have,
\begin{array}{rcl}
C+W=51.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=60.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=102.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=162.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&162\div6\\
&=&27.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&51-27\\
&=&24.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume William answered all the 51 questions correctly, and each correct answer has 4 marks, then William should score 204 marks,
\begin{array}{rcl}
51\times4=204.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since William only scored 60 marks, therefore William totally lost
\begin{array}{rcl}
204-60=144.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
144\div6=24.
\end{array}
The number of correct answers is
\begin{array}{rcl}
51-24=27.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 51, we have,
\begin{array}{rcl}
C+W=51.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=60.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=102.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=162.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&162\div6\\
&=&27.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&51-27\\
&=&24.\tag{6}
\end{array}
Isabella attended a South-East Asia Maths Olympaid (SEAMO). Isabella answered all 11 questions. For each correct answer, Isabella will get 3 marks. However, for each wrong answer, Isabella will be deducted by 1 mark(s). If Isabella scored 33 marks in total, how many questions did Isabella answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Isabella answered all the 11 questions correctly, and each correct answer has 3 marks, then Isabella should score 33 marks,
\begin{array}{rcl}
11\times3=33.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Isabella only scored 33 marks, therefore Isabella totally lost
\begin{array}{rcl}
33-33=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div4=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
11-0=11.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 11, we have,
\begin{array}{rcl}
C+W=11.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=33.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=44.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&44\div4\\
&=&11.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&11-11\\
&=&0.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Isabella answered all the 11 questions correctly, and each correct answer has 3 marks, then Isabella should score 33 marks,
\begin{array}{rcl}
11\times3=33.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Isabella only scored 33 marks, therefore Isabella totally lost
\begin{array}{rcl}
33-33=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div4=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
11-0=11.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 11, we have,
\begin{array}{rcl}
C+W=11.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=33.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=44.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&44\div4\\
&=&11.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&11-11\\
&=&0.\tag{6}
\end{array}
Sophia attended a Maths Competition. Sophia answered all 13 questions. For each correct answer, Sophia will get 4 marks. However, for each wrong answer, Sophia will be deducted by 1 mark(s). If Sophia scored 52 marks in total, how many questions did Sophia answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Sophia answered all the 13 questions correctly, and each correct answer has 4 marks, then Sophia should score 52 marks,
\begin{array}{rcl}
13\times4=52.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Sophia only scored 52 marks, therefore Sophia totally lost
\begin{array}{rcl}
52-52=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div5=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
13-0=13.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 13, we have,
\begin{array}{rcl}
C+W=13.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=52.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=65.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&65\div5\\
&=&13.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&13-13\\
&=&0.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Sophia answered all the 13 questions correctly, and each correct answer has 4 marks, then Sophia should score 52 marks,
\begin{array}{rcl}
13\times4=52.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Sophia only scored 52 marks, therefore Sophia totally lost
\begin{array}{rcl}
52-52=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div5=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
13-0=13.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 13, we have,
\begin{array}{rcl}
C+W=13.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=52.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=65.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&65\div5\\
&=&13.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&13-13\\
&=&0.\tag{6}
\end{array}
Mason attended a American Maths Olympiad (AMO). Mason answered all 66 questions. For each correct answer, Mason will get 8 marks. However, for each wrong answer, Mason will be deducted by 2 mark(s). If Mason scored 128 marks in total, how many questions did Mason answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Mason answered all the 66 questions correctly, and each correct answer has 8 marks, then Mason should score 528 marks,
\begin{array}{rcl}
66\times8=528.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Mason only scored 128 marks, therefore Mason totally lost
\begin{array}{rcl}
528-128=400.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
400\div10=40.
\end{array}
The number of correct answers is
\begin{array}{rcl}
66-40=26.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 66, we have,
\begin{array}{rcl}
C+W=66.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=128.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=132.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=260.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&260\div10\\
&=&26.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&66-26\\
&=&40.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Mason answered all the 66 questions correctly, and each correct answer has 8 marks, then Mason should score 528 marks,
\begin{array}{rcl}
66\times8=528.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Mason only scored 128 marks, therefore Mason totally lost
\begin{array}{rcl}
528-128=400.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
400\div10=40.
\end{array}
The number of correct answers is
\begin{array}{rcl}
66-40=26.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 66, we have,
\begin{array}{rcl}
C+W=66.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=128.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=132.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=260.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&260\div10\\
&=&26.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&66-26\\
&=&40.\tag{6}
\end{array}
William attended a Australian Maths Trust (AMT). William answered all 48 questions. For each correct answer, William will get 4 marks. However, for each wrong answer, William will be deducted by 2 mark(s). If William scored 72 marks in total, how many questions did William answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume William answered all the 48 questions correctly, and each correct answer has 4 marks, then William should score 192 marks,
\begin{array}{rcl}
48\times4=192.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since William only scored 72 marks, therefore William totally lost
\begin{array}{rcl}
192-72=120.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
120\div6=20.
\end{array}
The number of correct answers is
\begin{array}{rcl}
48-20=28.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 48, we have,
\begin{array}{rcl}
C+W=48.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=72.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=96.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=168.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&168\div6\\
&=&28.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&48-28\\
&=&20.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume William answered all the 48 questions correctly, and each correct answer has 4 marks, then William should score 192 marks,
\begin{array}{rcl}
48\times4=192.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since William only scored 72 marks, therefore William totally lost
\begin{array}{rcl}
192-72=120.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
120\div6=20.
\end{array}
The number of correct answers is
\begin{array}{rcl}
48-20=28.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 48, we have,
\begin{array}{rcl}
C+W=48.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=72.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=96.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=168.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&168\div6\\
&=&28.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&48-28\\
&=&20.\tag{6}
\end{array}
Jacob attended a English Spelling Bee Competition. Jacob answered all 52 questions. For each correct answer, Jacob will get 4 marks. However, for each wrong answer, Jacob will be deducted by 1 mark(s). If Jacob scored 68 marks in total, how many questions did Jacob answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Jacob answered all the 52 questions correctly, and each correct answer has 4 marks, then Jacob should score 208 marks,
\begin{array}{rcl}
52\times4=208.
\end{array}
For every question Jacob answered wrongly, Jacob will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Jacob only scored 68 marks, therefore Jacob totally lost
\begin{array}{rcl}
208-68=140.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
140\div5=28.
\end{array}
The number of correct answers is
\begin{array}{rcl}
52-28=24.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 52, we have,
\begin{array}{rcl}
C+W=52.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=68.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=120.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&120\div5\\
&=&24.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&52-24\\
&=&28.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Jacob answered all the 52 questions correctly, and each correct answer has 4 marks, then Jacob should score 208 marks,
\begin{array}{rcl}
52\times4=208.
\end{array}
For every question Jacob answered wrongly, Jacob will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Jacob only scored 68 marks, therefore Jacob totally lost
\begin{array}{rcl}
208-68=140.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
140\div5=28.
\end{array}
The number of correct answers is
\begin{array}{rcl}
52-28=24.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 52, we have,
\begin{array}{rcl}
C+W=52.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=68.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=120.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&120\div5\\
&=&24.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&52-24\\
&=&28.\tag{6}
\end{array}
Isabella attended a Singapore Maths Olympaid (SMO). Isabella answered all 69 questions. For each correct answer, Isabella will get 8 marks. However, for each wrong answer, Isabella will be deducted by 2 mark(s). If Isabella scored 152 marks in total, how many questions did Isabella answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Isabella answered all the 69 questions correctly, and each correct answer has 8 marks, then Isabella should score 552 marks,
\begin{array}{rcl}
69\times8=552.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Isabella only scored 152 marks, therefore Isabella totally lost
\begin{array}{rcl}
552-152=400.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
400\div10=40.
\end{array}
The number of correct answers is
\begin{array}{rcl}
69-40=29.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 69, we have,
\begin{array}{rcl}
C+W=69.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=152.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=138.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=290.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&290\div10\\
&=&29.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&69-29\\
&=&40.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Isabella answered all the 69 questions correctly, and each correct answer has 8 marks, then Isabella should score 552 marks,
\begin{array}{rcl}
69\times8=552.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Isabella only scored 152 marks, therefore Isabella totally lost
\begin{array}{rcl}
552-152=400.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
400\div10=40.
\end{array}
The number of correct answers is
\begin{array}{rcl}
69-40=29.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 69, we have,
\begin{array}{rcl}
C+W=69.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=152.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=138.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=290.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&290\div10\\
&=&29.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&69-29\\
&=&40.\tag{6}
\end{array}
James attended a Chinese Multiple Choices Test. James answered all 20 questions. For each correct answer, James will get 8 marks. However, for each wrong answer, James will be deducted by 2 mark(s). If James scored 160 marks in total, how many questions did James answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume James answered all the 20 questions correctly, and each correct answer has 8 marks, then James should score 160 marks,
\begin{array}{rcl}
20\times8=160.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since James only scored 160 marks, therefore James totally lost
\begin{array}{rcl}
160-160=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div10=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
20-0=20.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 20, we have,
\begin{array}{rcl}
C+W=20.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=160.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=40.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=200.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&200\div10\\
&=&20.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&20-20\\
&=&0.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume James answered all the 20 questions correctly, and each correct answer has 8 marks, then James should score 160 marks,
\begin{array}{rcl}
20\times8=160.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since James only scored 160 marks, therefore James totally lost
\begin{array}{rcl}
160-160=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div10=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
20-0=20.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 20, we have,
\begin{array}{rcl}
C+W=20.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=160.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=40.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=200.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&200\div10\\
&=&20.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&20-20\\
&=&0.\tag{6}
\end{array}
William attended a Maths Competition. William answered all 50 questions. For each correct answer, William will get 5 marks. However, for each wrong answer, William will be deducted by 1 mark(s). If William scored 100 marks in total, how many questions did William answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume William answered all the 50 questions correctly, and each correct answer has 5 marks, then William should score 250 marks,
\begin{array}{rcl}
50\times5=250.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since William only scored 100 marks, therefore William totally lost
\begin{array}{rcl}
250-100=150.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
150\div6=25.
\end{array}
The number of correct answers is
\begin{array}{rcl}
50-25=25.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 50, we have,
\begin{array}{rcl}
C+W=50.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=100.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=150.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&150\div6\\
&=&25.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&50-25\\
&=&25.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume William answered all the 50 questions correctly, and each correct answer has 5 marks, then William should score 250 marks,
\begin{array}{rcl}
50\times5=250.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since William only scored 100 marks, therefore William totally lost
\begin{array}{rcl}
250-100=150.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
150\div6=25.
\end{array}
The number of correct answers is
\begin{array}{rcl}
50-25=25.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 50, we have,
\begin{array}{rcl}
C+W=50.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=100.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=150.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&150\div6\\
&=&25.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&50-25\\
&=&25.\tag{6}
\end{array}
Isabella attended a Chinese Multiple Choices Test. Isabella answered all 54 questions. For each correct answer, Isabella will get 4 marks. However, for each wrong answer, Isabella will be deducted by 2 mark(s). If Isabella scored 72 marks in total, how many questions did Isabella answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Isabella answered all the 54 questions correctly, and each correct answer has 4 marks, then Isabella should score 216 marks,
\begin{array}{rcl}
54\times4=216.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Isabella only scored 72 marks, therefore Isabella totally lost
\begin{array}{rcl}
216-72=144.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
144\div6=24.
\end{array}
The number of correct answers is
\begin{array}{rcl}
54-24=30.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 54, we have,
\begin{array}{rcl}
C+W=54.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=72.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=108.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=180.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&180\div6\\
&=&30.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&54-30\\
&=&24.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Isabella answered all the 54 questions correctly, and each correct answer has 4 marks, then Isabella should score 216 marks,
\begin{array}{rcl}
54\times4=216.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Isabella only scored 72 marks, therefore Isabella totally lost
\begin{array}{rcl}
216-72=144.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
144\div6=24.
\end{array}
The number of correct answers is
\begin{array}{rcl}
54-24=30.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 54, we have,
\begin{array}{rcl}
C+W=54.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=72.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=108.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=180.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&180\div6\\
&=&30.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&54-30\\
&=&24.\tag{6}
\end{array}
Larry Page attended a American Maths Olympiad (AMO). Larry Page answered all 62 questions. For each correct answer, Larry Page will get 4 marks. However, for each wrong answer, Larry Page will be deducted by 1 mark(s). If Larry Page scored 68 marks in total, how many questions did Larry Page answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Larry Page answered all the 62 questions correctly, and each correct answer has 4 marks, then Larry Page should score 248 marks,
\begin{array}{rcl}
62\times4=248.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Larry Page only scored 68 marks, therefore Larry Page totally lost
\begin{array}{rcl}
248-68=180.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
180\div5=36.
\end{array}
The number of correct answers is
\begin{array}{rcl}
62-36=26.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 62, we have,
\begin{array}{rcl}
C+W=62.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=68.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=130.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&130\div5\\
&=&26.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&62-26\\
&=&36.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Larry Page answered all the 62 questions correctly, and each correct answer has 4 marks, then Larry Page should score 248 marks,
\begin{array}{rcl}
62\times4=248.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Larry Page only scored 68 marks, therefore Larry Page totally lost
\begin{array}{rcl}
248-68=180.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
180\div5=36.
\end{array}
The number of correct answers is
\begin{array}{rcl}
62-36=26.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 62, we have,
\begin{array}{rcl}
C+W=62.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=68.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=130.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&130\div5\\
&=&26.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&62-26\\
&=&36.\tag{6}
\end{array}
Isabella attended a English Spelling Bee Competition. Isabella answered all 21 questions. For each correct answer, Isabella will get 6 marks. However, for each wrong answer, Isabella will be deducted by 2 mark(s). If Isabella scored 78 marks in total, how many questions did Isabella answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Isabella answered all the 21 questions correctly, and each correct answer has 6 marks, then Isabella should score 126 marks,
\begin{array}{rcl}
21\times6=126.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Isabella only scored 78 marks, therefore Isabella totally lost
\begin{array}{rcl}
126-78=48.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
48\div8=6.
\end{array}
The number of correct answers is
\begin{array}{rcl}
21-6=15.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 21, we have,
\begin{array}{rcl}
C+W=21.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=78.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=42.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=120.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&120\div8\\
&=&15.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&21-15\\
&=&6.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Isabella answered all the 21 questions correctly, and each correct answer has 6 marks, then Isabella should score 126 marks,
\begin{array}{rcl}
21\times6=126.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Isabella only scored 78 marks, therefore Isabella totally lost
\begin{array}{rcl}
126-78=48.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
48\div8=6.
\end{array}
The number of correct answers is
\begin{array}{rcl}
21-6=15.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 21, we have,
\begin{array}{rcl}
C+W=21.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=78.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=42.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=120.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&120\div8\\
&=&15.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&21-15\\
&=&6.\tag{6}
\end{array}
Bill Gates attended a English Spelling Bee Competition. Bill Gates answered all 57 questions. For each correct answer, Bill Gates will get 6 marks. However, for each wrong answer, Bill Gates will be deducted by 2 mark(s). If Bill Gates scored 102 marks in total, how many questions did Bill Gates answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Bill Gates answered all the 57 questions correctly, and each correct answer has 6 marks, then Bill Gates should score 342 marks,
\begin{array}{rcl}
57\times6=342.
\end{array}
For every question Bill Gates answered wrongly, Bill Gates will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Bill Gates only scored 102 marks, therefore Bill Gates totally lost
\begin{array}{rcl}
342-102=240.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
240\div8=30.
\end{array}
The number of correct answers is
\begin{array}{rcl}
57-30=27.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 57, we have,
\begin{array}{rcl}
C+W=57.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=102.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=114.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=216.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&216\div8\\
&=&27.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&57-27\\
&=&30.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Bill Gates answered all the 57 questions correctly, and each correct answer has 6 marks, then Bill Gates should score 342 marks,
\begin{array}{rcl}
57\times6=342.
\end{array}
For every question Bill Gates answered wrongly, Bill Gates will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Bill Gates only scored 102 marks, therefore Bill Gates totally lost
\begin{array}{rcl}
342-102=240.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
240\div8=30.
\end{array}
The number of correct answers is
\begin{array}{rcl}
57-30=27.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 57, we have,
\begin{array}{rcl}
C+W=57.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=102.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=114.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=216.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&216\div8\\
&=&27.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&57-27\\
&=&30.\tag{6}
\end{array}
Larry Page attended a South-East Asia Maths Olympaid (SEAMO). Larry Page answered all 46 questions. For each correct answer, Larry Page will get 10 marks. However, for each wrong answer, Larry Page will be deducted by 2 mark(s). If Larry Page scored 100 marks in total, how many questions did Larry Page answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Larry Page answered all the 46 questions correctly, and each correct answer has 10 marks, then Larry Page should score 460 marks,
\begin{array}{rcl}
46\times10=460.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Larry Page only scored 100 marks, therefore Larry Page totally lost
\begin{array}{rcl}
460-100=360.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
360\div12=30.
\end{array}
The number of correct answers is
\begin{array}{rcl}
46-30=16.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 46, we have,
\begin{array}{rcl}
C+W=46.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=100.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=92.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=192.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&192\div12\\
&=&16.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&46-16\\
&=&30.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Larry Page answered all the 46 questions correctly, and each correct answer has 10 marks, then Larry Page should score 460 marks,
\begin{array}{rcl}
46\times10=460.
\end{array}
For every question Larry Page answered wrongly, Larry Page will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Larry Page only scored 100 marks, therefore Larry Page totally lost
\begin{array}{rcl}
460-100=360.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
360\div12=30.
\end{array}
The number of correct answers is
\begin{array}{rcl}
46-30=16.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 46, we have,
\begin{array}{rcl}
C+W=46.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=100.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=92.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=192.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&192\div12\\
&=&16.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&46-16\\
&=&30.\tag{6}
\end{array}
Benjamin attended a Maths Competition. Benjamin answered all 103 questions. For each correct answer, Benjamin will get 10 marks. However, for each wrong answer, Benjamin will be deducted by 2 mark(s). If Benjamin scored 190 marks in total, how many questions did Benjamin answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Benjamin answered all the 103 questions correctly, and each correct answer has 10 marks, then Benjamin should score 1030 marks,
\begin{array}{rcl}
103\times10=1030.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Benjamin only scored 190 marks, therefore Benjamin totally lost
\begin{array}{rcl}
1030-190=840.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
840\div12=70.
\end{array}
The number of correct answers is
\begin{array}{rcl}
103-70=33.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 103, we have,
\begin{array}{rcl}
C+W=103.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=190.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=206.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=396.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&396\div12\\
&=&33.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&103-33\\
&=&70.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Benjamin answered all the 103 questions correctly, and each correct answer has 10 marks, then Benjamin should score 1030 marks,
\begin{array}{rcl}
103\times10=1030.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Benjamin only scored 190 marks, therefore Benjamin totally lost
\begin{array}{rcl}
1030-190=840.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
840\div12=70.
\end{array}
The number of correct answers is
\begin{array}{rcl}
103-70=33.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 103, we have,
\begin{array}{rcl}
C+W=103.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=190.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=206.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=396.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&396\div12\\
&=&33.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&103-33\\
&=&70.\tag{6}
\end{array}
Olivia attended a South-East Asia Maths Olympaid (SEAMO). Olivia answered all 71 questions. For each correct answer, Olivia will get 4 marks. However, for each wrong answer, Olivia will be deducted by 2 mark(s). If Olivia scored 44 marks in total, how many questions did Olivia answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Olivia answered all the 71 questions correctly, and each correct answer has 4 marks, then Olivia should score 284 marks,
\begin{array}{rcl}
71\times4=284.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Olivia only scored 44 marks, therefore Olivia totally lost
\begin{array}{rcl}
284-44=240.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
240\div6=40.
\end{array}
The number of correct answers is
\begin{array}{rcl}
71-40=31.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 71, we have,
\begin{array}{rcl}
C+W=71.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=44.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=142.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=186.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&186\div6\\
&=&31.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&71-31\\
&=&40.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Olivia answered all the 71 questions correctly, and each correct answer has 4 marks, then Olivia should score 284 marks,
\begin{array}{rcl}
71\times4=284.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Olivia only scored 44 marks, therefore Olivia totally lost
\begin{array}{rcl}
284-44=240.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
240\div6=40.
\end{array}
The number of correct answers is
\begin{array}{rcl}
71-40=31.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 71, we have,
\begin{array}{rcl}
C+W=71.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=44.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=142.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=186.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&186\div6\\
&=&31.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&71-31\\
&=&40.\tag{6}
\end{array}
Olivia attended a Maths Competition. Olivia answered all 53 questions. For each correct answer, Olivia will get 4 marks. However, for each wrong answer, Olivia will be deducted by 1 mark(s). If Olivia scored 52 marks in total, how many questions did Olivia answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Olivia answered all the 53 questions correctly, and each correct answer has 4 marks, then Olivia should score 212 marks,
\begin{array}{rcl}
53\times4=212.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Olivia only scored 52 marks, therefore Olivia totally lost
\begin{array}{rcl}
212-52=160.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
160\div5=32.
\end{array}
The number of correct answers is
\begin{array}{rcl}
53-32=21.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 53, we have,
\begin{array}{rcl}
C+W=53.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=52.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=105.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&105\div5\\
&=&21.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&53-21\\
&=&32.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Olivia answered all the 53 questions correctly, and each correct answer has 4 marks, then Olivia should score 212 marks,
\begin{array}{rcl}
53\times4=212.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Olivia only scored 52 marks, therefore Olivia totally lost
\begin{array}{rcl}
212-52=160.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
160\div5=32.
\end{array}
The number of correct answers is
\begin{array}{rcl}
53-32=21.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 53, we have,
\begin{array}{rcl}
C+W=53.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=52.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=105.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&105\div5\\
&=&21.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&53-21\\
&=&32.\tag{6}
\end{array}
Bill Gates attended a South-East Asia Maths Olympaid (SEAMO). Bill Gates answered all 22 questions. For each correct answer, Bill Gates will get 4 marks. However, for each wrong answer, Bill Gates will be deducted by 2 mark(s). If Bill Gates scored 64 marks in total, how many questions did Bill Gates answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Bill Gates answered all the 22 questions correctly, and each correct answer has 4 marks, then Bill Gates should score 88 marks,
\begin{array}{rcl}
22\times4=88.
\end{array}
For every question Bill Gates answered wrongly, Bill Gates will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Bill Gates only scored 64 marks, therefore Bill Gates totally lost
\begin{array}{rcl}
88-64=24.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
24\div6=4.
\end{array}
The number of correct answers is
\begin{array}{rcl}
22-4=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 22, we have,
\begin{array}{rcl}
C+W=22.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=64.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=44.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=108.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&108\div6\\
&=&18.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&22-18\\
&=&4.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Bill Gates answered all the 22 questions correctly, and each correct answer has 4 marks, then Bill Gates should score 88 marks,
\begin{array}{rcl}
22\times4=88.
\end{array}
For every question Bill Gates answered wrongly, Bill Gates will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Bill Gates only scored 64 marks, therefore Bill Gates totally lost
\begin{array}{rcl}
88-64=24.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
24\div6=4.
\end{array}
The number of correct answers is
\begin{array}{rcl}
22-4=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 22, we have,
\begin{array}{rcl}
C+W=22.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=64.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=44.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=108.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&108\div6\\
&=&18.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&22-18\\
&=&4.\tag{6}
\end{array}
Benjamin attended a Chinese Multiple Choices Test. Benjamin answered all 122 questions. For each correct answer, Benjamin will get 10 marks. However, for each wrong answer, Benjamin will be deducted by 2 mark(s). If Benjamin scored 140 marks in total, how many questions did Benjamin answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Benjamin answered all the 122 questions correctly, and each correct answer has 10 marks, then Benjamin should score 1220 marks,
\begin{array}{rcl}
122\times10=1220.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Benjamin only scored 140 marks, therefore Benjamin totally lost
\begin{array}{rcl}
1220-140=1080.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
1080\div12=90.
\end{array}
The number of correct answers is
\begin{array}{rcl}
122-90=32.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 122, we have,
\begin{array}{rcl}
C+W=122.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=140.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=244.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=384.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&384\div12\\
&=&32.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&122-32\\
&=&90.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Benjamin answered all the 122 questions correctly, and each correct answer has 10 marks, then Benjamin should score 1220 marks,
\begin{array}{rcl}
122\times10=1220.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Benjamin only scored 140 marks, therefore Benjamin totally lost
\begin{array}{rcl}
1220-140=1080.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
1080\div12=90.
\end{array}
The number of correct answers is
\begin{array}{rcl}
122-90=32.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 122, we have,
\begin{array}{rcl}
C+W=122.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=140.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=244.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=384.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&384\div12\\
&=&32.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&122-32\\
&=&90.\tag{6}
\end{array}
Bill Gates attended a American Maths Olympiad (AMO). Bill Gates answered all 16 questions. For each correct answer, Bill Gates will get 8 marks. However, for each wrong answer, Bill Gates will be deducted by 2 mark(s). If Bill Gates scored 128 marks in total, how many questions did Bill Gates answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Bill Gates answered all the 16 questions correctly, and each correct answer has 8 marks, then Bill Gates should score 128 marks,
\begin{array}{rcl}
16\times8=128.
\end{array}
For every question Bill Gates answered wrongly, Bill Gates will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Bill Gates only scored 128 marks, therefore Bill Gates totally lost
\begin{array}{rcl}
128-128=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div10=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
16-0=16.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 16, we have,
\begin{array}{rcl}
C+W=16.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=128.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=32.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=160.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&160\div10\\
&=&16.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&16-16\\
&=&0.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Bill Gates answered all the 16 questions correctly, and each correct answer has 8 marks, then Bill Gates should score 128 marks,
\begin{array}{rcl}
16\times8=128.
\end{array}
For every question Bill Gates answered wrongly, Bill Gates will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Bill Gates only scored 128 marks, therefore Bill Gates totally lost
\begin{array}{rcl}
128-128=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div10=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
16-0=16.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 16, we have,
\begin{array}{rcl}
C+W=16.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=128.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=32.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=160.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&160\div10\\
&=&16.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&16-16\\
&=&0.\tag{6}
\end{array}
William attended a Singapore Maths Olympaid (SMO). William answered all 40 questions. For each correct answer, William will get 3 marks. However, for each wrong answer, William will be deducted by 1 mark(s). If William scored 48 marks in total, how many questions did William answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume William answered all the 40 questions correctly, and each correct answer has 3 marks, then William should score 120 marks,
\begin{array}{rcl}
40\times3=120.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since William only scored 48 marks, therefore William totally lost
\begin{array}{rcl}
120-48=72.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
72\div4=18.
\end{array}
The number of correct answers is
\begin{array}{rcl}
40-18=22.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 40, we have,
\begin{array}{rcl}
C+W=40.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=48.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=88.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&88\div4\\
&=&22.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&40-22\\
&=&18.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume William answered all the 40 questions correctly, and each correct answer has 3 marks, then William should score 120 marks,
\begin{array}{rcl}
40\times3=120.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since William only scored 48 marks, therefore William totally lost
\begin{array}{rcl}
120-48=72.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
72\div4=18.
\end{array}
The number of correct answers is
\begin{array}{rcl}
40-18=22.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 40, we have,
\begin{array}{rcl}
C+W=40.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=48.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=88.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&88\div4\\
&=&22.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&40-22\\
&=&18.\tag{6}
\end{array}
Isabella attended a American Maths Olympiad (AMO). Isabella answered all 115 questions. For each correct answer, Isabella will get 10 marks. However, for each wrong answer, Isabella will be deducted by 2 mark(s). If Isabella scored 190 marks in total, how many questions did Isabella answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Isabella answered all the 115 questions correctly, and each correct answer has 10 marks, then Isabella should score 1150 marks,
\begin{array}{rcl}
115\times10=1150.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Isabella only scored 190 marks, therefore Isabella totally lost
\begin{array}{rcl}
1150-190=960.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
960\div12=80.
\end{array}
The number of correct answers is
\begin{array}{rcl}
115-80=35.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 115, we have,
\begin{array}{rcl}
C+W=115.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=190.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=230.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=420.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&420\div12\\
&=&35.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&115-35\\
&=&80.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Isabella answered all the 115 questions correctly, and each correct answer has 10 marks, then Isabella should score 1150 marks,
\begin{array}{rcl}
115\times10=1150.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Isabella only scored 190 marks, therefore Isabella totally lost
\begin{array}{rcl}
1150-190=960.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
960\div12=80.
\end{array}
The number of correct answers is
\begin{array}{rcl}
115-80=35.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 115, we have,
\begin{array}{rcl}
C+W=115.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=190.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=230.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=420.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&420\div12\\
&=&35.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&115-35\\
&=&80.\tag{6}
\end{array}
Mason attended a Australian Maths Trust (AMT). Mason answered all 44 questions. For each correct answer, Mason will get 4 marks. However, for each wrong answer, Mason will be deducted by 2 mark(s). If Mason scored 80 marks in total, how many questions did Mason answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Mason answered all the 44 questions correctly, and each correct answer has 4 marks, then Mason should score 176 marks,
\begin{array}{rcl}
44\times4=176.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Mason only scored 80 marks, therefore Mason totally lost
\begin{array}{rcl}
176-80=96.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
96\div6=16.
\end{array}
The number of correct answers is
\begin{array}{rcl}
44-16=28.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 44, we have,
\begin{array}{rcl}
C+W=44.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=80.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=88.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=168.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&168\div6\\
&=&28.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&44-28\\
&=&16.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Mason answered all the 44 questions correctly, and each correct answer has 4 marks, then Mason should score 176 marks,
\begin{array}{rcl}
44\times4=176.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Mason only scored 80 marks, therefore Mason totally lost
\begin{array}{rcl}
176-80=96.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
96\div6=16.
\end{array}
The number of correct answers is
\begin{array}{rcl}
44-16=28.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 44, we have,
\begin{array}{rcl}
C+W=44.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=80.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=88.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=168.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&168\div6\\
&=&28.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&44-28\\
&=&16.\tag{6}
\end{array}
Emma attended a Maths Competition. Emma answered all 38 questions. For each correct answer, Emma will get 8 marks. However, for each wrong answer, Emma will be deducted by 2 mark(s). If Emma scored 144 marks in total, how many questions did Emma answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Emma answered all the 38 questions correctly, and each correct answer has 8 marks, then Emma should score 304 marks,
\begin{array}{rcl}
38\times8=304.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Emma only scored 144 marks, therefore Emma totally lost
\begin{array}{rcl}
304-144=160.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
160\div10=16.
\end{array}
The number of correct answers is
\begin{array}{rcl}
38-16=22.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 38, we have,
\begin{array}{rcl}
C+W=38.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=144.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=76.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=220.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&220\div10\\
&=&22.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&38-22\\
&=&16.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Emma answered all the 38 questions correctly, and each correct answer has 8 marks, then Emma should score 304 marks,
\begin{array}{rcl}
38\times8=304.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Emma only scored 144 marks, therefore Emma totally lost
\begin{array}{rcl}
304-144=160.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
160\div10=16.
\end{array}
The number of correct answers is
\begin{array}{rcl}
38-16=22.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 38, we have,
\begin{array}{rcl}
C+W=38.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=144.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=76.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=220.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&220\div10\\
&=&22.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&38-22\\
&=&16.\tag{6}
\end{array}
Olivia attended a American Maths Olympiad (AMO). Olivia answered all 47 questions. For each correct answer, Olivia will get 2 marks. However, for each wrong answer, Olivia will be deducted by 1 mark(s). If Olivia scored 34 marks in total, how many questions did Olivia answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Olivia answered all the 47 questions correctly, and each correct answer has 2 marks, then Olivia should score 94 marks,
\begin{array}{rcl}
47\times2=94.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Olivia only scored 34 marks, therefore Olivia totally lost
\begin{array}{rcl}
94-34=60.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
60\div3=20.
\end{array}
The number of correct answers is
\begin{array}{rcl}
47-20=27.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 47, we have,
\begin{array}{rcl}
C+W=47.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=34.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=81.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&81\div3\\
&=&27.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&47-27\\
&=&20.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Olivia answered all the 47 questions correctly, and each correct answer has 2 marks, then Olivia should score 94 marks,
\begin{array}{rcl}
47\times2=94.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Olivia only scored 34 marks, therefore Olivia totally lost
\begin{array}{rcl}
94-34=60.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
60\div3=20.
\end{array}
The number of correct answers is
\begin{array}{rcl}
47-20=27.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 47, we have,
\begin{array}{rcl}
C+W=47.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=34.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=81.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&81\div3\\
&=&27.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&47-27\\
&=&20.\tag{6}
\end{array}
Olivia attended a Chinese Multiple Choices Test. Olivia answered all 46 questions. For each correct answer, Olivia will get 5 marks. However, for each wrong answer, Olivia will be deducted by 1 mark(s). If Olivia scored 50 marks in total, how many questions did Olivia answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Olivia answered all the 46 questions correctly, and each correct answer has 5 marks, then Olivia should score 230 marks,
\begin{array}{rcl}
46\times5=230.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Olivia only scored 50 marks, therefore Olivia totally lost
\begin{array}{rcl}
230-50=180.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
180\div6=30.
\end{array}
The number of correct answers is
\begin{array}{rcl}
46-30=16.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 46, we have,
\begin{array}{rcl}
C+W=46.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=50.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=96.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&96\div6\\
&=&16.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&46-16\\
&=&30.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Olivia answered all the 46 questions correctly, and each correct answer has 5 marks, then Olivia should score 230 marks,
\begin{array}{rcl}
46\times5=230.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Olivia only scored 50 marks, therefore Olivia totally lost
\begin{array}{rcl}
230-50=180.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
180\div6=30.
\end{array}
The number of correct answers is
\begin{array}{rcl}
46-30=16.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 46, we have,
\begin{array}{rcl}
C+W=46.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=50.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=96.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&96\div6\\
&=&16.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&46-16\\
&=&30.\tag{6}
\end{array}
Noah attended a Maths Competition. Noah answered all 15 questions. For each correct answer, Noah will get 2 marks. However, for each wrong answer, Noah will be deducted by 1 mark(s). If Noah scored 30 marks in total, how many questions did Noah answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Noah answered all the 15 questions correctly, and each correct answer has 2 marks, then Noah should score 30 marks,
\begin{array}{rcl}
15\times2=30.
\end{array}
For every question Noah answered wrongly, Noah will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Noah only scored 30 marks, therefore Noah totally lost
\begin{array}{rcl}
30-30=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div3=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
15-0=15.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 15, we have,
\begin{array}{rcl}
C+W=15.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=30.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=45.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&45\div3\\
&=&15.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&15-15\\
&=&0.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Noah answered all the 15 questions correctly, and each correct answer has 2 marks, then Noah should score 30 marks,
\begin{array}{rcl}
15\times2=30.
\end{array}
For every question Noah answered wrongly, Noah will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Noah only scored 30 marks, therefore Noah totally lost
\begin{array}{rcl}
30-30=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div3=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
15-0=15.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 15, we have,
\begin{array}{rcl}
C+W=15.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=30.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=45.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&45\div3\\
&=&15.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&15-15\\
&=&0.\tag{6}
\end{array}
Noah attended a American Maths Olympiad (AMO). Noah answered all 63 questions. For each correct answer, Noah will get 4 marks. However, for each wrong answer, Noah will be deducted by 2 mark(s). If Noah scored 60 marks in total, how many questions did Noah answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Noah answered all the 63 questions correctly, and each correct answer has 4 marks, then Noah should score 252 marks,
\begin{array}{rcl}
63\times4=252.
\end{array}
For every question Noah answered wrongly, Noah will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Noah only scored 60 marks, therefore Noah totally lost
\begin{array}{rcl}
252-60=192.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
192\div6=32.
\end{array}
The number of correct answers is
\begin{array}{rcl}
63-32=31.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 63, we have,
\begin{array}{rcl}
C+W=63.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=60.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=126.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=186.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&186\div6\\
&=&31.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&63-31\\
&=&32.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Noah answered all the 63 questions correctly, and each correct answer has 4 marks, then Noah should score 252 marks,
\begin{array}{rcl}
63\times4=252.
\end{array}
For every question Noah answered wrongly, Noah will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Noah only scored 60 marks, therefore Noah totally lost
\begin{array}{rcl}
252-60=192.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
192\div6=32.
\end{array}
The number of correct answers is
\begin{array}{rcl}
63-32=31.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 63, we have,
\begin{array}{rcl}
C+W=63.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=60.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=126.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=186.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&186\div6\\
&=&31.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&63-31\\
&=&32.\tag{6}
\end{array}
William attended a Maths Competition. William answered all 46 questions. For each correct answer, William will get 4 marks. However, for each wrong answer, William will be deducted by 2 mark(s). If William scored 40 marks in total, how many questions did William answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume William answered all the 46 questions correctly, and each correct answer has 4 marks, then William should score 184 marks,
\begin{array}{rcl}
46\times4=184.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since William only scored 40 marks, therefore William totally lost
\begin{array}{rcl}
184-40=144.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
144\div6=24.
\end{array}
The number of correct answers is
\begin{array}{rcl}
46-24=22.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 46, we have,
\begin{array}{rcl}
C+W=46.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=40.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=92.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=132.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&132\div6\\
&=&22.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&46-22\\
&=&24.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume William answered all the 46 questions correctly, and each correct answer has 4 marks, then William should score 184 marks,
\begin{array}{rcl}
46\times4=184.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since William only scored 40 marks, therefore William totally lost
\begin{array}{rcl}
184-40=144.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
144\div6=24.
\end{array}
The number of correct answers is
\begin{array}{rcl}
46-24=22.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 46, we have,
\begin{array}{rcl}
C+W=46.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=40.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=92.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=132.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&132\div6\\
&=&22.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&46-22\\
&=&24.\tag{6}
\end{array}
Olivia attended a Maths Competition. Olivia answered all 18 questions. For each correct answer, Olivia will get 5 marks. However, for each wrong answer, Olivia will be deducted by 1 mark(s). If Olivia scored 60 marks in total, how many questions did Olivia answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Olivia answered all the 18 questions correctly, and each correct answer has 5 marks, then Olivia should score 90 marks,
\begin{array}{rcl}
18\times5=90.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Olivia only scored 60 marks, therefore Olivia totally lost
\begin{array}{rcl}
90-60=30.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
30\div6=5.
\end{array}
The number of correct answers is
\begin{array}{rcl}
18-5=13.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 18, we have,
\begin{array}{rcl}
C+W=18.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=60.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=78.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&78\div6\\
&=&13.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&18-13\\
&=&5.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Olivia answered all the 18 questions correctly, and each correct answer has 5 marks, then Olivia should score 90 marks,
\begin{array}{rcl}
18\times5=90.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Olivia only scored 60 marks, therefore Olivia totally lost
\begin{array}{rcl}
90-60=30.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
30\div6=5.
\end{array}
The number of correct answers is
\begin{array}{rcl}
18-5=13.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 18, we have,
\begin{array}{rcl}
C+W=18.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=60.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=78.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&78\div6\\
&=&13.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&18-13\\
&=&5.\tag{6}
\end{array}
James attended a American Maths Olympiad (AMO). James answered all 76 questions. For each correct answer, James will get 8 marks. However, for each wrong answer, James will be deducted by 2 mark(s). If James scored 128 marks in total, how many questions did James answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume James answered all the 76 questions correctly, and each correct answer has 8 marks, then James should score 608 marks,
\begin{array}{rcl}
76\times8=608.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since James only scored 128 marks, therefore James totally lost
\begin{array}{rcl}
608-128=480.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
480\div10=48.
\end{array}
The number of correct answers is
\begin{array}{rcl}
76-48=28.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 76, we have,
\begin{array}{rcl}
C+W=76.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=128.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=152.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=280.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&280\div10\\
&=&28.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&76-28\\
&=&48.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume James answered all the 76 questions correctly, and each correct answer has 8 marks, then James should score 608 marks,
\begin{array}{rcl}
76\times8=608.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since James only scored 128 marks, therefore James totally lost
\begin{array}{rcl}
608-128=480.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
480\div10=48.
\end{array}
The number of correct answers is
\begin{array}{rcl}
76-48=28.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 76, we have,
\begin{array}{rcl}
C+W=76.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=128.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=152.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=280.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&280\div10\\
&=&28.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&76-28\\
&=&48.\tag{6}
\end{array}
Mason attended a Chinese Multiple Choices Test. Mason answered all 63 questions. For each correct answer, Mason will get 4 marks. However, for each wrong answer, Mason will be deducted by 1 mark(s). If Mason scored 52 marks in total, how many questions did Mason answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Mason answered all the 63 questions correctly, and each correct answer has 4 marks, then Mason should score 252 marks,
\begin{array}{rcl}
63\times4=252.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Mason only scored 52 marks, therefore Mason totally lost
\begin{array}{rcl}
252-52=200.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
200\div5=40.
\end{array}
The number of correct answers is
\begin{array}{rcl}
63-40=23.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 63, we have,
\begin{array}{rcl}
C+W=63.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=52.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=115.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&115\div5\\
&=&23.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&63-23\\
&=&40.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Mason answered all the 63 questions correctly, and each correct answer has 4 marks, then Mason should score 252 marks,
\begin{array}{rcl}
63\times4=252.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Mason only scored 52 marks, therefore Mason totally lost
\begin{array}{rcl}
252-52=200.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
200\div5=40.
\end{array}
The number of correct answers is
\begin{array}{rcl}
63-40=23.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 63, we have,
\begin{array}{rcl}
C+W=63.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=52.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=115.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&115\div5\\
&=&23.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&63-23\\
&=&40.\tag{6}
\end{array}
William attended a Chinese Multiple Choices Test. William answered all 101 questions. For each correct answer, William will get 8 marks. However, for each wrong answer, William will be deducted by 2 mark(s). If William scored 88 marks in total, how many questions did William answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume William answered all the 101 questions correctly, and each correct answer has 8 marks, then William should score 808 marks,
\begin{array}{rcl}
101\times8=808.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since William only scored 88 marks, therefore William totally lost
\begin{array}{rcl}
808-88=720.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
720\div10=72.
\end{array}
The number of correct answers is
\begin{array}{rcl}
101-72=29.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 101, we have,
\begin{array}{rcl}
C+W=101.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=88.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=202.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=290.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&290\div10\\
&=&29.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&101-29\\
&=&72.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume William answered all the 101 questions correctly, and each correct answer has 8 marks, then William should score 808 marks,
\begin{array}{rcl}
101\times8=808.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since William only scored 88 marks, therefore William totally lost
\begin{array}{rcl}
808-88=720.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
720\div10=72.
\end{array}
The number of correct answers is
\begin{array}{rcl}
101-72=29.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 101, we have,
\begin{array}{rcl}
C+W=101.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=88.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=202.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=290.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&290\div10\\
&=&29.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&101-29\\
&=&72.\tag{6}
\end{array}
Liam attended a American Maths Olympiad (AMO). Liam answered all 27 questions. For each correct answer, Liam will get 2 marks. However, for each wrong answer, Liam will be deducted by 1 mark(s). If Liam scored 24 marks in total, how many questions did Liam answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Liam answered all the 27 questions correctly, and each correct answer has 2 marks, then Liam should score 54 marks,
\begin{array}{rcl}
27\times2=54.
\end{array}
For every question Liam answered wrongly, Liam will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Liam only scored 24 marks, therefore Liam totally lost
\begin{array}{rcl}
54-24=30.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
30\div3=10.
\end{array}
The number of correct answers is
\begin{array}{rcl}
27-10=17.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 27, we have,
\begin{array}{rcl}
C+W=27.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=24.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=51.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&51\div3\\
&=&17.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&27-17\\
&=&10.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Liam answered all the 27 questions correctly, and each correct answer has 2 marks, then Liam should score 54 marks,
\begin{array}{rcl}
27\times2=54.
\end{array}
For every question Liam answered wrongly, Liam will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Liam only scored 24 marks, therefore Liam totally lost
\begin{array}{rcl}
54-24=30.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
30\div3=10.
\end{array}
The number of correct answers is
\begin{array}{rcl}
27-10=17.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 27, we have,
\begin{array}{rcl}
C+W=27.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=24.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=51.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&51\div3\\
&=&17.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&27-17\\
&=&10.\tag{6}
\end{array}
Jacob attended a Chinese Multiple Choices Test. Jacob answered all 27 questions. For each correct answer, Jacob will get 4 marks. However, for each wrong answer, Jacob will be deducted by 2 mark(s). If Jacob scored 60 marks in total, how many questions did Jacob answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Jacob answered all the 27 questions correctly, and each correct answer has 4 marks, then Jacob should score 108 marks,
\begin{array}{rcl}
27\times4=108.
\end{array}
For every question Jacob answered wrongly, Jacob will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Jacob only scored 60 marks, therefore Jacob totally lost
\begin{array}{rcl}
108-60=48.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
48\div6=8.
\end{array}
The number of correct answers is
\begin{array}{rcl}
27-8=19.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 27, we have,
\begin{array}{rcl}
C+W=27.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=60.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=54.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=114.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&114\div6\\
&=&19.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&27-19\\
&=&8.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Jacob answered all the 27 questions correctly, and each correct answer has 4 marks, then Jacob should score 108 marks,
\begin{array}{rcl}
27\times4=108.
\end{array}
For every question Jacob answered wrongly, Jacob will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Jacob only scored 60 marks, therefore Jacob totally lost
\begin{array}{rcl}
108-60=48.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
48\div6=8.
\end{array}
The number of correct answers is
\begin{array}{rcl}
27-8=19.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 27, we have,
\begin{array}{rcl}
C+W=27.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=60.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=54.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=114.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&114\div6\\
&=&19.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&27-19\\
&=&8.\tag{6}
\end{array}
William attended a Maths Competition. William answered all 56 questions. For each correct answer, William will get 3 marks. However, for each wrong answer, William will be deducted by 1 mark(s). If William scored 48 marks in total, how many questions did William answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume William answered all the 56 questions correctly, and each correct answer has 3 marks, then William should score 168 marks,
\begin{array}{rcl}
56\times3=168.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since William only scored 48 marks, therefore William totally lost
\begin{array}{rcl}
168-48=120.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
120\div4=30.
\end{array}
The number of correct answers is
\begin{array}{rcl}
56-30=26.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 56, we have,
\begin{array}{rcl}
C+W=56.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=48.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=104.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&104\div4\\
&=&26.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&56-26\\
&=&30.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume William answered all the 56 questions correctly, and each correct answer has 3 marks, then William should score 168 marks,
\begin{array}{rcl}
56\times3=168.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since William only scored 48 marks, therefore William totally lost
\begin{array}{rcl}
168-48=120.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
120\div4=30.
\end{array}
The number of correct answers is
\begin{array}{rcl}
56-30=26.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 56, we have,
\begin{array}{rcl}
C+W=56.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=48.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=104.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&104\div4\\
&=&26.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&56-26\\
&=&30.\tag{6}
\end{array}
Benjamin attended a Singapore Maths Olympaid (SMO). Benjamin answered all 25 questions. For each correct answer, Benjamin will get 4 marks. However, for each wrong answer, Benjamin will be deducted by 1 mark(s). If Benjamin scored 40 marks in total, how many questions did Benjamin answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Benjamin answered all the 25 questions correctly, and each correct answer has 4 marks, then Benjamin should score 100 marks,
\begin{array}{rcl}
25\times4=100.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Benjamin only scored 40 marks, therefore Benjamin totally lost
\begin{array}{rcl}
100-40=60.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
60\div5=12.
\end{array}
The number of correct answers is
\begin{array}{rcl}
25-12=13.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 25, we have,
\begin{array}{rcl}
C+W=25.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=40.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=65.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&65\div5\\
&=&13.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&25-13\\
&=&12.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Benjamin answered all the 25 questions correctly, and each correct answer has 4 marks, then Benjamin should score 100 marks,
\begin{array}{rcl}
25\times4=100.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Benjamin only scored 40 marks, therefore Benjamin totally lost
\begin{array}{rcl}
100-40=60.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
60\div5=12.
\end{array}
The number of correct answers is
\begin{array}{rcl}
25-12=13.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 25, we have,
\begin{array}{rcl}
C+W=25.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=40.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=65.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&65\div5\\
&=&13.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&25-13\\
&=&12.\tag{6}
\end{array}
William attended a American Maths Olympiad (AMO). William answered all 25 questions. For each correct answer, William will get 2 marks. However, for each wrong answer, William will be deducted by 1 mark(s). If William scored 38 marks in total, how many questions did William answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume William answered all the 25 questions correctly, and each correct answer has 2 marks, then William should score 50 marks,
\begin{array}{rcl}
25\times2=50.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since William only scored 38 marks, therefore William totally lost
\begin{array}{rcl}
50-38=12.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
12\div3=4.
\end{array}
The number of correct answers is
\begin{array}{rcl}
25-4=21.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 25, we have,
\begin{array}{rcl}
C+W=25.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=38.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=63.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&63\div3\\
&=&21.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&25-21\\
&=&4.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume William answered all the 25 questions correctly, and each correct answer has 2 marks, then William should score 50 marks,
\begin{array}{rcl}
25\times2=50.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since William only scored 38 marks, therefore William totally lost
\begin{array}{rcl}
50-38=12.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
12\div3=4.
\end{array}
The number of correct answers is
\begin{array}{rcl}
25-4=21.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 25, we have,
\begin{array}{rcl}
C+W=25.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=38.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=63.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&63\div3\\
&=&21.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&25-21\\
&=&4.\tag{6}
\end{array}
Bill Gates attended a South-East Asia Maths Olympaid (SEAMO). Bill Gates answered all 23 questions. For each correct answer, Bill Gates will get 2 marks. However, for each wrong answer, Bill Gates will be deducted by 1 mark(s). If Bill Gates scored 22 marks in total, how many questions did Bill Gates answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Bill Gates answered all the 23 questions correctly, and each correct answer has 2 marks, then Bill Gates should score 46 marks,
\begin{array}{rcl}
23\times2=46.
\end{array}
For every question Bill Gates answered wrongly, Bill Gates will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Bill Gates only scored 22 marks, therefore Bill Gates totally lost
\begin{array}{rcl}
46-22=24.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
24\div3=8.
\end{array}
The number of correct answers is
\begin{array}{rcl}
23-8=15.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 23, we have,
\begin{array}{rcl}
C+W=23.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=22.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=45.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&45\div3\\
&=&15.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&23-15\\
&=&8.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Bill Gates answered all the 23 questions correctly, and each correct answer has 2 marks, then Bill Gates should score 46 marks,
\begin{array}{rcl}
23\times2=46.
\end{array}
For every question Bill Gates answered wrongly, Bill Gates will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Bill Gates only scored 22 marks, therefore Bill Gates totally lost
\begin{array}{rcl}
46-22=24.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
24\div3=8.
\end{array}
The number of correct answers is
\begin{array}{rcl}
23-8=15.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 23, we have,
\begin{array}{rcl}
C+W=23.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=22.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=45.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&45\div3\\
&=&15.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&23-15\\
&=&8.\tag{6}
\end{array}
Sophia attended a Australian Maths Trust (AMT). Sophia answered all 19 questions. For each correct answer, Sophia will get 5 marks. However, for each wrong answer, Sophia will be deducted by 1 mark(s). If Sophia scored 65 marks in total, how many questions did Sophia answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Sophia answered all the 19 questions correctly, and each correct answer has 5 marks, then Sophia should score 95 marks,
\begin{array}{rcl}
19\times5=95.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Sophia only scored 65 marks, therefore Sophia totally lost
\begin{array}{rcl}
95-65=30.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
30\div6=5.
\end{array}
The number of correct answers is
\begin{array}{rcl}
19-5=14.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 19, we have,
\begin{array}{rcl}
C+W=19.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=65.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=84.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&84\div6\\
&=&14.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&19-14\\
&=&5.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Sophia answered all the 19 questions correctly, and each correct answer has 5 marks, then Sophia should score 95 marks,
\begin{array}{rcl}
19\times5=95.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Sophia only scored 65 marks, therefore Sophia totally lost
\begin{array}{rcl}
95-65=30.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
30\div6=5.
\end{array}
The number of correct answers is
\begin{array}{rcl}
19-5=14.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 19, we have,
\begin{array}{rcl}
C+W=19.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=65.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=84.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&84\div6\\
&=&14.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&19-14\\
&=&5.\tag{6}
\end{array}
Olivia attended a American Maths Olympiad (AMO). Olivia answered all 52 questions. For each correct answer, Olivia will get 8 marks. However, for each wrong answer, Olivia will be deducted by 2 mark(s). If Olivia scored 96 marks in total, how many questions did Olivia answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Olivia answered all the 52 questions correctly, and each correct answer has 8 marks, then Olivia should score 416 marks,
\begin{array}{rcl}
52\times8=416.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Olivia only scored 96 marks, therefore Olivia totally lost
\begin{array}{rcl}
416-96=320.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
320\div10=32.
\end{array}
The number of correct answers is
\begin{array}{rcl}
52-32=20.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 52, we have,
\begin{array}{rcl}
C+W=52.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=96.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=104.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=200.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&200\div10\\
&=&20.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&52-20\\
&=&32.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Olivia answered all the 52 questions correctly, and each correct answer has 8 marks, then Olivia should score 416 marks,
\begin{array}{rcl}
52\times8=416.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Olivia only scored 96 marks, therefore Olivia totally lost
\begin{array}{rcl}
416-96=320.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
320\div10=32.
\end{array}
The number of correct answers is
\begin{array}{rcl}
52-32=20.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 52, we have,
\begin{array}{rcl}
C+W=52.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=96.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=104.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=200.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&200\div10\\
&=&20.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&52-20\\
&=&32.\tag{6}
\end{array}
Sophia attended a Australian Maths Trust (AMT). Sophia answered all 72 questions. For each correct answer, Sophia will get 8 marks. However, for each wrong answer, Sophia will be deducted by 2 mark(s). If Sophia scored 96 marks in total, how many questions did Sophia answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Sophia answered all the 72 questions correctly, and each correct answer has 8 marks, then Sophia should score 576 marks,
\begin{array}{rcl}
72\times8=576.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Sophia only scored 96 marks, therefore Sophia totally lost
\begin{array}{rcl}
576-96=480.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
480\div10=48.
\end{array}
The number of correct answers is
\begin{array}{rcl}
72-48=24.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 72, we have,
\begin{array}{rcl}
C+W=72.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=96.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=144.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=240.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&240\div10\\
&=&24.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&72-24\\
&=&48.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Sophia answered all the 72 questions correctly, and each correct answer has 8 marks, then Sophia should score 576 marks,
\begin{array}{rcl}
72\times8=576.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Sophia only scored 96 marks, therefore Sophia totally lost
\begin{array}{rcl}
576-96=480.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
480\div10=48.
\end{array}
The number of correct answers is
\begin{array}{rcl}
72-48=24.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 72, we have,
\begin{array}{rcl}
C+W=72.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=96.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=144.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=240.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&240\div10\\
&=&24.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&72-24\\
&=&48.\tag{6}
\end{array}
William attended a Maths Competition. William answered all 17 questions. For each correct answer, William will get 8 marks. However, for each wrong answer, William will be deducted by 2 mark(s). If William scored 136 marks in total, how many questions did William answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume William answered all the 17 questions correctly, and each correct answer has 8 marks, then William should score 136 marks,
\begin{array}{rcl}
17\times8=136.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since William only scored 136 marks, therefore William totally lost
\begin{array}{rcl}
136-136=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div10=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
17-0=17.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 17, we have,
\begin{array}{rcl}
C+W=17.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=136.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=34.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=170.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&170\div10\\
&=&17.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&17-17\\
&=&0.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume William answered all the 17 questions correctly, and each correct answer has 8 marks, then William should score 136 marks,
\begin{array}{rcl}
17\times8=136.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since William only scored 136 marks, therefore William totally lost
\begin{array}{rcl}
136-136=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div10=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
17-0=17.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 17, we have,
\begin{array}{rcl}
C+W=17.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=136.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=34.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=170.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&170\div10\\
&=&17.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&17-17\\
&=&0.\tag{6}
\end{array}
Emma attended a Maths Competition. Emma answered all 50 questions. For each correct answer, Emma will get 5 marks. However, for each wrong answer, Emma will be deducted by 1 mark(s). If Emma scored 70 marks in total, how many questions did Emma answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Emma answered all the 50 questions correctly, and each correct answer has 5 marks, then Emma should score 250 marks,
\begin{array}{rcl}
50\times5=250.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Emma only scored 70 marks, therefore Emma totally lost
\begin{array}{rcl}
250-70=180.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
180\div6=30.
\end{array}
The number of correct answers is
\begin{array}{rcl}
50-30=20.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 50, we have,
\begin{array}{rcl}
C+W=50.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=70.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=120.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&120\div6\\
&=&20.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&50-20\\
&=&30.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Emma answered all the 50 questions correctly, and each correct answer has 5 marks, then Emma should score 250 marks,
\begin{array}{rcl}
50\times5=250.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Emma only scored 70 marks, therefore Emma totally lost
\begin{array}{rcl}
250-70=180.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
180\div6=30.
\end{array}
The number of correct answers is
\begin{array}{rcl}
50-30=20.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 50, we have,
\begin{array}{rcl}
C+W=50.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=70.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=120.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&120\div6\\
&=&20.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&50-20\\
&=&30.\tag{6}
\end{array}
Noah attended a South-East Asia Maths Olympaid (SEAMO). Noah answered all 24 questions. For each correct answer, Noah will get 5 marks. However, for each wrong answer, Noah will be deducted by 1 mark(s). If Noah scored 60 marks in total, how many questions did Noah answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Noah answered all the 24 questions correctly, and each correct answer has 5 marks, then Noah should score 120 marks,
\begin{array}{rcl}
24\times5=120.
\end{array}
For every question Noah answered wrongly, Noah will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Noah only scored 60 marks, therefore Noah totally lost
\begin{array}{rcl}
120-60=60.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
60\div6=10.
\end{array}
The number of correct answers is
\begin{array}{rcl}
24-10=14.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 24, we have,
\begin{array}{rcl}
C+W=24.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=60.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=84.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&84\div6\\
&=&14.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&24-14\\
&=&10.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Noah answered all the 24 questions correctly, and each correct answer has 5 marks, then Noah should score 120 marks,
\begin{array}{rcl}
24\times5=120.
\end{array}
For every question Noah answered wrongly, Noah will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Noah only scored 60 marks, therefore Noah totally lost
\begin{array}{rcl}
120-60=60.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
60\div6=10.
\end{array}
The number of correct answers is
\begin{array}{rcl}
24-10=14.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 24, we have,
\begin{array}{rcl}
C+W=24.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=60.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=84.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&84\div6\\
&=&14.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&24-14\\
&=&10.\tag{6}
\end{array}
Isabella attended a American Maths Olympiad (AMO). Isabella answered all 28 questions. For each correct answer, Isabella will get 2 marks. However, for each wrong answer, Isabella will be deducted by 1 mark(s). If Isabella scored 26 marks in total, how many questions did Isabella answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Isabella answered all the 28 questions correctly, and each correct answer has 2 marks, then Isabella should score 56 marks,
\begin{array}{rcl}
28\times2=56.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Isabella only scored 26 marks, therefore Isabella totally lost
\begin{array}{rcl}
56-26=30.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
30\div3=10.
\end{array}
The number of correct answers is
\begin{array}{rcl}
28-10=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 28, we have,
\begin{array}{rcl}
C+W=28.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=26.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=54.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&54\div3\\
&=&18.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&28-18\\
&=&10.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Isabella answered all the 28 questions correctly, and each correct answer has 2 marks, then Isabella should score 56 marks,
\begin{array}{rcl}
28\times2=56.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Isabella only scored 26 marks, therefore Isabella totally lost
\begin{array}{rcl}
56-26=30.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
30\div3=10.
\end{array}
The number of correct answers is
\begin{array}{rcl}
28-10=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 28, we have,
\begin{array}{rcl}
C+W=28.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=26.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=54.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&54\div3\\
&=&18.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&28-18\\
&=&10.\tag{6}
\end{array}
Jacob attended a English Spelling Bee Competition. Jacob answered all 48 questions. For each correct answer, Jacob will get 3 marks. However, for each wrong answer, Jacob will be deducted by 1 mark(s). If Jacob scored 60 marks in total, how many questions did Jacob answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Jacob answered all the 48 questions correctly, and each correct answer has 3 marks, then Jacob should score 144 marks,
\begin{array}{rcl}
48\times3=144.
\end{array}
For every question Jacob answered wrongly, Jacob will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Jacob only scored 60 marks, therefore Jacob totally lost
\begin{array}{rcl}
144-60=84.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
84\div4=21.
\end{array}
The number of correct answers is
\begin{array}{rcl}
48-21=27.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 48, we have,
\begin{array}{rcl}
C+W=48.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=60.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=108.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&108\div4\\
&=&27.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&48-27\\
&=&21.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Jacob answered all the 48 questions correctly, and each correct answer has 3 marks, then Jacob should score 144 marks,
\begin{array}{rcl}
48\times3=144.
\end{array}
For every question Jacob answered wrongly, Jacob will lose,
\begin{array}{rcl}
3+1=4.
\end{array}
marks.
Since Jacob only scored 60 marks, therefore Jacob totally lost
\begin{array}{rcl}
144-60=84.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
84\div4=21.
\end{array}
The number of correct answers is
\begin{array}{rcl}
48-21=27.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 48, we have,
\begin{array}{rcl}
C+W=48.\tag{1}
\end{array}
Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
3C-1W=60.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
4C=108.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&108\div4\\
&=&27.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&48-27\\
&=&21.\tag{6}
\end{array}
Benjamin attended a Maths Competition. Benjamin answered all 72 questions. For each correct answer, Benjamin will get 8 marks. However, for each wrong answer, Benjamin will be deducted by 2 mark(s). If Benjamin scored 96 marks in total, how many questions did Benjamin answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Benjamin answered all the 72 questions correctly, and each correct answer has 8 marks, then Benjamin should score 576 marks,
\begin{array}{rcl}
72\times8=576.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Benjamin only scored 96 marks, therefore Benjamin totally lost
\begin{array}{rcl}
576-96=480.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
480\div10=48.
\end{array}
The number of correct answers is
\begin{array}{rcl}
72-48=24.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 72, we have,
\begin{array}{rcl}
C+W=72.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=96.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=144.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=240.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&240\div10\\
&=&24.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&72-24\\
&=&48.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Benjamin answered all the 72 questions correctly, and each correct answer has 8 marks, then Benjamin should score 576 marks,
\begin{array}{rcl}
72\times8=576.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Benjamin only scored 96 marks, therefore Benjamin totally lost
\begin{array}{rcl}
576-96=480.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
480\div10=48.
\end{array}
The number of correct answers is
\begin{array}{rcl}
72-48=24.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 72, we have,
\begin{array}{rcl}
C+W=72.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=96.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=144.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=240.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&240\div10\\
&=&24.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&72-24\\
&=&48.\tag{6}
\end{array}
Isabella attended a American Maths Olympiad (AMO). Isabella answered all 26 questions. For each correct answer, Isabella will get 10 marks. However, for each wrong answer, Isabella will be deducted by 2 mark(s). If Isabella scored 140 marks in total, how many questions did Isabella answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Isabella answered all the 26 questions correctly, and each correct answer has 10 marks, then Isabella should score 260 marks,
\begin{array}{rcl}
26\times10=260.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Isabella only scored 140 marks, therefore Isabella totally lost
\begin{array}{rcl}
260-140=120.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
120\div12=10.
\end{array}
The number of correct answers is
\begin{array}{rcl}
26-10=16.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 26, we have,
\begin{array}{rcl}
C+W=26.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=140.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=52.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=192.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&192\div12\\
&=&16.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&26-16\\
&=&10.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Isabella answered all the 26 questions correctly, and each correct answer has 10 marks, then Isabella should score 260 marks,
\begin{array}{rcl}
26\times10=260.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Isabella only scored 140 marks, therefore Isabella totally lost
\begin{array}{rcl}
260-140=120.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
120\div12=10.
\end{array}
The number of correct answers is
\begin{array}{rcl}
26-10=16.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 26, we have,
\begin{array}{rcl}
C+W=26.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=140.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=52.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=192.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&192\div12\\
&=&16.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&26-16\\
&=&10.\tag{6}
\end{array}
Bill Gates attended a South-East Asia Maths Olympaid (SEAMO). Bill Gates answered all 80 questions. For each correct answer, Bill Gates will get 6 marks. However, for each wrong answer, Bill Gates will be deducted by 2 mark(s). If Bill Gates scored 96 marks in total, how many questions did Bill Gates answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Bill Gates answered all the 80 questions correctly, and each correct answer has 6 marks, then Bill Gates should score 480 marks,
\begin{array}{rcl}
80\times6=480.
\end{array}
For every question Bill Gates answered wrongly, Bill Gates will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Bill Gates only scored 96 marks, therefore Bill Gates totally lost
\begin{array}{rcl}
480-96=384.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
384\div8=48.
\end{array}
The number of correct answers is
\begin{array}{rcl}
80-48=32.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 80, we have,
\begin{array}{rcl}
C+W=80.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=96.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=160.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=256.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&256\div8\\
&=&32.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&80-32\\
&=&48.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Bill Gates answered all the 80 questions correctly, and each correct answer has 6 marks, then Bill Gates should score 480 marks,
\begin{array}{rcl}
80\times6=480.
\end{array}
For every question Bill Gates answered wrongly, Bill Gates will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Bill Gates only scored 96 marks, therefore Bill Gates totally lost
\begin{array}{rcl}
480-96=384.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
384\div8=48.
\end{array}
The number of correct answers is
\begin{array}{rcl}
80-48=32.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 80, we have,
\begin{array}{rcl}
C+W=80.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=96.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=160.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=256.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&256\div8\\
&=&32.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&80-32\\
&=&48.\tag{6}
\end{array}
William attended a American Maths Olympiad (AMO). William answered all 70 questions. For each correct answer, William will get 5 marks. However, for each wrong answer, William will be deducted by 1 mark(s). If William scored 50 marks in total, how many questions did William answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume William answered all the 70 questions correctly, and each correct answer has 5 marks, then William should score 350 marks,
\begin{array}{rcl}
70\times5=350.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since William only scored 50 marks, therefore William totally lost
\begin{array}{rcl}
350-50=300.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
300\div6=50.
\end{array}
The number of correct answers is
\begin{array}{rcl}
70-50=20.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 70, we have,
\begin{array}{rcl}
C+W=70.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=50.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=120.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&120\div6\\
&=&20.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&70-20\\
&=&50.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume William answered all the 70 questions correctly, and each correct answer has 5 marks, then William should score 350 marks,
\begin{array}{rcl}
70\times5=350.
\end{array}
For every question William answered wrongly, William will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since William only scored 50 marks, therefore William totally lost
\begin{array}{rcl}
350-50=300.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
300\div6=50.
\end{array}
The number of correct answers is
\begin{array}{rcl}
70-50=20.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 70, we have,
\begin{array}{rcl}
C+W=70.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=50.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=120.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&120\div6\\
&=&20.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&70-20\\
&=&50.\tag{6}
\end{array}
Jacob attended a American Maths Olympiad (AMO). Jacob answered all 35 questions. For each correct answer, Jacob will get 2 marks. However, for each wrong answer, Jacob will be deducted by 1 mark(s). If Jacob scored 40 marks in total, how many questions did Jacob answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Jacob answered all the 35 questions correctly, and each correct answer has 2 marks, then Jacob should score 70 marks,
\begin{array}{rcl}
35\times2=70.
\end{array}
For every question Jacob answered wrongly, Jacob will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Jacob only scored 40 marks, therefore Jacob totally lost
\begin{array}{rcl}
70-40=30.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
30\div3=10.
\end{array}
The number of correct answers is
\begin{array}{rcl}
35-10=25.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 35, we have,
\begin{array}{rcl}
C+W=35.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=40.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=75.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&75\div3\\
&=&25.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&35-25\\
&=&10.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Jacob answered all the 35 questions correctly, and each correct answer has 2 marks, then Jacob should score 70 marks,
\begin{array}{rcl}
35\times2=70.
\end{array}
For every question Jacob answered wrongly, Jacob will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Jacob only scored 40 marks, therefore Jacob totally lost
\begin{array}{rcl}
70-40=30.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
30\div3=10.
\end{array}
The number of correct answers is
\begin{array}{rcl}
35-10=25.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 35, we have,
\begin{array}{rcl}
C+W=35.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=40.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=75.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&75\div3\\
&=&25.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&35-25\\
&=&10.\tag{6}
\end{array}
Liam attended a English Spelling Bee Competition. Liam answered all 22 questions. For each correct answer, Liam will get 2 marks. However, for each wrong answer, Liam will be deducted by 1 mark(s). If Liam scored 38 marks in total, how many questions did Liam answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Liam answered all the 22 questions correctly, and each correct answer has 2 marks, then Liam should score 44 marks,
\begin{array}{rcl}
22\times2=44.
\end{array}
For every question Liam answered wrongly, Liam will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Liam only scored 38 marks, therefore Liam totally lost
\begin{array}{rcl}
44-38=6.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
6\div3=2.
\end{array}
The number of correct answers is
\begin{array}{rcl}
22-2=20.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 22, we have,
\begin{array}{rcl}
C+W=22.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=38.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=60.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&60\div3\\
&=&20.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&22-20\\
&=&2.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Liam answered all the 22 questions correctly, and each correct answer has 2 marks, then Liam should score 44 marks,
\begin{array}{rcl}
22\times2=44.
\end{array}
For every question Liam answered wrongly, Liam will lose,
\begin{array}{rcl}
2+1=3.
\end{array}
marks.
Since Liam only scored 38 marks, therefore Liam totally lost
\begin{array}{rcl}
44-38=6.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
6\div3=2.
\end{array}
The number of correct answers is
\begin{array}{rcl}
22-2=20.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 22, we have,
\begin{array}{rcl}
C+W=22.\tag{1}
\end{array}
Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
2C-1W=38.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
3C=60.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&60\div3\\
&=&20.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&22-20\\
&=&2.\tag{6}
\end{array}
Noah attended a Chinese Multiple Choices Test. Noah answered all 106 questions. For each correct answer, Noah will get 10 marks. However, for each wrong answer, Noah will be deducted by 2 mark(s). If Noah scored 100 marks in total, how many questions did Noah answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Noah answered all the 106 questions correctly, and each correct answer has 10 marks, then Noah should score 1060 marks,
\begin{array}{rcl}
106\times10=1060.
\end{array}
For every question Noah answered wrongly, Noah will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Noah only scored 100 marks, therefore Noah totally lost
\begin{array}{rcl}
1060-100=960.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
960\div12=80.
\end{array}
The number of correct answers is
\begin{array}{rcl}
106-80=26.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 106, we have,
\begin{array}{rcl}
C+W=106.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=100.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=212.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=312.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&312\div12\\
&=&26.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&106-26\\
&=&80.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Noah answered all the 106 questions correctly, and each correct answer has 10 marks, then Noah should score 1060 marks,
\begin{array}{rcl}
106\times10=1060.
\end{array}
For every question Noah answered wrongly, Noah will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Noah only scored 100 marks, therefore Noah totally lost
\begin{array}{rcl}
1060-100=960.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
960\div12=80.
\end{array}
The number of correct answers is
\begin{array}{rcl}
106-80=26.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 106, we have,
\begin{array}{rcl}
C+W=106.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=100.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=212.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=312.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&312\div12\\
&=&26.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&106-26\\
&=&80.\tag{6}
\end{array}
Olivia attended a Maths Competition. Olivia answered all 47 questions. For each correct answer, Olivia will get 4 marks. However, for each wrong answer, Olivia will be deducted by 1 mark(s). If Olivia scored 68 marks in total, how many questions did Olivia answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Olivia answered all the 47 questions correctly, and each correct answer has 4 marks, then Olivia should score 188 marks,
\begin{array}{rcl}
47\times4=188.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Olivia only scored 68 marks, therefore Olivia totally lost
\begin{array}{rcl}
188-68=120.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
120\div5=24.
\end{array}
The number of correct answers is
\begin{array}{rcl}
47-24=23.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 47, we have,
\begin{array}{rcl}
C+W=47.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=68.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=115.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&115\div5\\
&=&23.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&47-23\\
&=&24.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Olivia answered all the 47 questions correctly, and each correct answer has 4 marks, then Olivia should score 188 marks,
\begin{array}{rcl}
47\times4=188.
\end{array}
For every question Olivia answered wrongly, Olivia will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Olivia only scored 68 marks, therefore Olivia totally lost
\begin{array}{rcl}
188-68=120.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
120\div5=24.
\end{array}
The number of correct answers is
\begin{array}{rcl}
47-24=23.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 47, we have,
\begin{array}{rcl}
C+W=47.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=68.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=115.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&115\div5\\
&=&23.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&47-23\\
&=&24.\tag{6}
\end{array}
Liam attended a South-East Asia Maths Olympaid (SEAMO). Liam answered all 75 questions. For each correct answer, Liam will get 5 marks. However, for each wrong answer, Liam will be deducted by 1 mark(s). If Liam scored 75 marks in total, how many questions did Liam answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Liam answered all the 75 questions correctly, and each correct answer has 5 marks, then Liam should score 375 marks,
\begin{array}{rcl}
75\times5=375.
\end{array}
For every question Liam answered wrongly, Liam will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Liam only scored 75 marks, therefore Liam totally lost
\begin{array}{rcl}
375-75=300.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
300\div6=50.
\end{array}
The number of correct answers is
\begin{array}{rcl}
75-50=25.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 75, we have,
\begin{array}{rcl}
C+W=75.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=75.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=150.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&150\div6\\
&=&25.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&75-25\\
&=&50.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Liam answered all the 75 questions correctly, and each correct answer has 5 marks, then Liam should score 375 marks,
\begin{array}{rcl}
75\times5=375.
\end{array}
For every question Liam answered wrongly, Liam will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Liam only scored 75 marks, therefore Liam totally lost
\begin{array}{rcl}
375-75=300.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
300\div6=50.
\end{array}
The number of correct answers is
\begin{array}{rcl}
75-50=25.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 75, we have,
\begin{array}{rcl}
C+W=75.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=75.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=150.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&150\div6\\
&=&25.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&75-25\\
&=&50.\tag{6}
\end{array}
Sophia attended a Singapore Maths Olympaid (SMO). Sophia answered all 57 questions. For each correct answer, Sophia will get 4 marks. However, for each wrong answer, Sophia will be deducted by 1 mark(s). If Sophia scored 48 marks in total, how many questions did Sophia answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Sophia answered all the 57 questions correctly, and each correct answer has 4 marks, then Sophia should score 228 marks,
\begin{array}{rcl}
57\times4=228.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Sophia only scored 48 marks, therefore Sophia totally lost
\begin{array}{rcl}
228-48=180.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
180\div5=36.
\end{array}
The number of correct answers is
\begin{array}{rcl}
57-36=21.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 57, we have,
\begin{array}{rcl}
C+W=57.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=48.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=105.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&105\div5\\
&=&21.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&57-21\\
&=&36.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Sophia answered all the 57 questions correctly, and each correct answer has 4 marks, then Sophia should score 228 marks,
\begin{array}{rcl}
57\times4=228.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Sophia only scored 48 marks, therefore Sophia totally lost
\begin{array}{rcl}
228-48=180.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
180\div5=36.
\end{array}
The number of correct answers is
\begin{array}{rcl}
57-36=21.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 57, we have,
\begin{array}{rcl}
C+W=57.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=48.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=105.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&105\div5\\
&=&21.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&57-21\\
&=&36.\tag{6}
\end{array}
Mason attended a Australian Maths Trust (AMT). Mason answered all 36 questions. For each correct answer, Mason will get 4 marks. However, for each wrong answer, Mason will be deducted by 1 mark(s). If Mason scored 44 marks in total, how many questions did Mason answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Mason answered all the 36 questions correctly, and each correct answer has 4 marks, then Mason should score 144 marks,
\begin{array}{rcl}
36\times4=144.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Mason only scored 44 marks, therefore Mason totally lost
\begin{array}{rcl}
144-44=100.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
100\div5=20.
\end{array}
The number of correct answers is
\begin{array}{rcl}
36-20=16.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 36, we have,
\begin{array}{rcl}
C+W=36.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=44.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=80.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&80\div5\\
&=&16.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&36-16\\
&=&20.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Mason answered all the 36 questions correctly, and each correct answer has 4 marks, then Mason should score 144 marks,
\begin{array}{rcl}
36\times4=144.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Mason only scored 44 marks, therefore Mason totally lost
\begin{array}{rcl}
144-44=100.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
100\div5=20.
\end{array}
The number of correct answers is
\begin{array}{rcl}
36-20=16.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 36, we have,
\begin{array}{rcl}
C+W=36.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=44.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=80.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&80\div5\\
&=&16.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&36-16\\
&=&20.\tag{6}
\end{array}
Bill Gates attended a Maths Competition. Bill Gates answered all 57 questions. For each correct answer, Bill Gates will get 4 marks. However, for each wrong answer, Bill Gates will be deducted by 1 mark(s). If Bill Gates scored 68 marks in total, how many questions did Bill Gates answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Bill Gates answered all the 57 questions correctly, and each correct answer has 4 marks, then Bill Gates should score 228 marks,
\begin{array}{rcl}
57\times4=228.
\end{array}
For every question Bill Gates answered wrongly, Bill Gates will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Bill Gates only scored 68 marks, therefore Bill Gates totally lost
\begin{array}{rcl}
228-68=160.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
160\div5=32.
\end{array}
The number of correct answers is
\begin{array}{rcl}
57-32=25.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 57, we have,
\begin{array}{rcl}
C+W=57.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=68.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=125.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&125\div5\\
&=&25.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&57-25\\
&=&32.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Bill Gates answered all the 57 questions correctly, and each correct answer has 4 marks, then Bill Gates should score 228 marks,
\begin{array}{rcl}
57\times4=228.
\end{array}
For every question Bill Gates answered wrongly, Bill Gates will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Bill Gates only scored 68 marks, therefore Bill Gates totally lost
\begin{array}{rcl}
228-68=160.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
160\div5=32.
\end{array}
The number of correct answers is
\begin{array}{rcl}
57-32=25.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 57, we have,
\begin{array}{rcl}
C+W=57.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=68.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=125.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&125\div5\\
&=&25.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&57-25\\
&=&32.\tag{6}
\end{array}
Benjamin attended a Maths Competition. Benjamin answered all 84 questions. For each correct answer, Benjamin will get 10 marks. However, for each wrong answer, Benjamin will be deducted by 2 mark(s). If Benjamin scored 120 marks in total, how many questions did Benjamin answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Benjamin answered all the 84 questions correctly, and each correct answer has 10 marks, then Benjamin should score 840 marks,
\begin{array}{rcl}
84\times10=840.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Benjamin only scored 120 marks, therefore Benjamin totally lost
\begin{array}{rcl}
840-120=720.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
720\div12=60.
\end{array}
The number of correct answers is
\begin{array}{rcl}
84-60=24.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 84, we have,
\begin{array}{rcl}
C+W=84.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=120.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=168.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=288.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&288\div12\\
&=&24.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&84-24\\
&=&60.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Benjamin answered all the 84 questions correctly, and each correct answer has 10 marks, then Benjamin should score 840 marks,
\begin{array}{rcl}
84\times10=840.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Benjamin only scored 120 marks, therefore Benjamin totally lost
\begin{array}{rcl}
840-120=720.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
720\div12=60.
\end{array}
The number of correct answers is
\begin{array}{rcl}
84-60=24.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 84, we have,
\begin{array}{rcl}
C+W=84.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=120.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=168.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=288.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&288\div12\\
&=&24.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&84-24\\
&=&60.\tag{6}
\end{array}
Isabella attended a South-East Asia Maths Olympaid (SEAMO). Isabella answered all 69 questions. For each correct answer, Isabella will get 4 marks. However, for each wrong answer, Isabella will be deducted by 1 mark(s). If Isabella scored 76 marks in total, how many questions did Isabella answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Isabella answered all the 69 questions correctly, and each correct answer has 4 marks, then Isabella should score 276 marks,
\begin{array}{rcl}
69\times4=276.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Isabella only scored 76 marks, therefore Isabella totally lost
\begin{array}{rcl}
276-76=200.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
200\div5=40.
\end{array}
The number of correct answers is
\begin{array}{rcl}
69-40=29.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 69, we have,
\begin{array}{rcl}
C+W=69.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=76.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=145.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&145\div5\\
&=&29.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&69-29\\
&=&40.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Isabella answered all the 69 questions correctly, and each correct answer has 4 marks, then Isabella should score 276 marks,
\begin{array}{rcl}
69\times4=276.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Isabella only scored 76 marks, therefore Isabella totally lost
\begin{array}{rcl}
276-76=200.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
200\div5=40.
\end{array}
The number of correct answers is
\begin{array}{rcl}
69-40=29.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 69, we have,
\begin{array}{rcl}
C+W=69.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=76.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=145.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&145\div5\\
&=&29.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&69-29\\
&=&40.\tag{6}
\end{array}
Emma attended a Singapore Maths Olympaid (SMO). Emma answered all 55 questions. For each correct answer, Emma will get 4 marks. However, for each wrong answer, Emma will be deducted by 2 mark(s). If Emma scored 76 marks in total, how many questions did Emma answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Emma answered all the 55 questions correctly, and each correct answer has 4 marks, then Emma should score 220 marks,
\begin{array}{rcl}
55\times4=220.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Emma only scored 76 marks, therefore Emma totally lost
\begin{array}{rcl}
220-76=144.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
144\div6=24.
\end{array}
The number of correct answers is
\begin{array}{rcl}
55-24=31.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 55, we have,
\begin{array}{rcl}
C+W=55.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=76.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=110.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=186.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&186\div6\\
&=&31.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&55-31\\
&=&24.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Emma answered all the 55 questions correctly, and each correct answer has 4 marks, then Emma should score 220 marks,
\begin{array}{rcl}
55\times4=220.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Emma only scored 76 marks, therefore Emma totally lost
\begin{array}{rcl}
220-76=144.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
144\div6=24.
\end{array}
The number of correct answers is
\begin{array}{rcl}
55-24=31.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 55, we have,
\begin{array}{rcl}
C+W=55.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=76.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=110.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=186.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&186\div6\\
&=&31.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&55-31\\
&=&24.\tag{6}
\end{array}
Ava attended a American Maths Olympiad (AMO). Ava answered all 32 questions. For each correct answer, Ava will get 4 marks. However, for each wrong answer, Ava will be deducted by 1 mark(s). If Ava scored 48 marks in total, how many questions did Ava answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Ava answered all the 32 questions correctly, and each correct answer has 4 marks, then Ava should score 128 marks,
\begin{array}{rcl}
32\times4=128.
\end{array}
For every question Ava answered wrongly, Ava will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Ava only scored 48 marks, therefore Ava totally lost
\begin{array}{rcl}
128-48=80.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
80\div5=16.
\end{array}
The number of correct answers is
\begin{array}{rcl}
32-16=16.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 32, we have,
\begin{array}{rcl}
C+W=32.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=48.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=80.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&80\div5\\
&=&16.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&32-16\\
&=&16.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Ava answered all the 32 questions correctly, and each correct answer has 4 marks, then Ava should score 128 marks,
\begin{array}{rcl}
32\times4=128.
\end{array}
For every question Ava answered wrongly, Ava will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Ava only scored 48 marks, therefore Ava totally lost
\begin{array}{rcl}
128-48=80.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
80\div5=16.
\end{array}
The number of correct answers is
\begin{array}{rcl}
32-16=16.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 32, we have,
\begin{array}{rcl}
C+W=32.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=48.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=80.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&80\div5\\
&=&16.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&32-16\\
&=&16.\tag{6}
\end{array}
Jacob attended a South-East Asia Maths Olympaid (SEAMO). Jacob answered all 92 questions. For each correct answer, Jacob will get 10 marks. However, for each wrong answer, Jacob will be deducted by 2 mark(s). If Jacob scored 200 marks in total, how many questions did Jacob answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Jacob answered all the 92 questions correctly, and each correct answer has 10 marks, then Jacob should score 920 marks,
\begin{array}{rcl}
92\times10=920.
\end{array}
For every question Jacob answered wrongly, Jacob will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Jacob only scored 200 marks, therefore Jacob totally lost
\begin{array}{rcl}
920-200=720.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
720\div12=60.
\end{array}
The number of correct answers is
\begin{array}{rcl}
92-60=32.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 92, we have,
\begin{array}{rcl}
C+W=92.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=200.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=184.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=384.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&384\div12\\
&=&32.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&92-32\\
&=&60.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Jacob answered all the 92 questions correctly, and each correct answer has 10 marks, then Jacob should score 920 marks,
\begin{array}{rcl}
92\times10=920.
\end{array}
For every question Jacob answered wrongly, Jacob will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Jacob only scored 200 marks, therefore Jacob totally lost
\begin{array}{rcl}
920-200=720.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
720\div12=60.
\end{array}
The number of correct answers is
\begin{array}{rcl}
92-60=32.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 92, we have,
\begin{array}{rcl}
C+W=92.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=200.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=184.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=384.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&384\div12\\
&=&32.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&92-32\\
&=&60.\tag{6}
\end{array}
Noah attended a Singapore Maths Olympaid (SMO). Noah answered all 30 questions. For each correct answer, Noah will get 8 marks. However, for each wrong answer, Noah will be deducted by 2 mark(s). If Noah scored 80 marks in total, how many questions did Noah answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Noah answered all the 30 questions correctly, and each correct answer has 8 marks, then Noah should score 240 marks,
\begin{array}{rcl}
30\times8=240.
\end{array}
For every question Noah answered wrongly, Noah will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Noah only scored 80 marks, therefore Noah totally lost
\begin{array}{rcl}
240-80=160.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
160\div10=16.
\end{array}
The number of correct answers is
\begin{array}{rcl}
30-16=14.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 30, we have,
\begin{array}{rcl}
C+W=30.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=80.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=60.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=140.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&140\div10\\
&=&14.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&30-14\\
&=&16.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Noah answered all the 30 questions correctly, and each correct answer has 8 marks, then Noah should score 240 marks,
\begin{array}{rcl}
30\times8=240.
\end{array}
For every question Noah answered wrongly, Noah will lose,
\begin{array}{rcl}
8+2=10.
\end{array}
marks.
Since Noah only scored 80 marks, therefore Noah totally lost
\begin{array}{rcl}
240-80=160.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
160\div10=16.
\end{array}
The number of correct answers is
\begin{array}{rcl}
30-16=14.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 30, we have,
\begin{array}{rcl}
C+W=30.\tag{1}
\end{array}
Since for every correct answer gives 8 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
8C-2W=80.\tag{2}
\end{array}
Multiplying both sides of (1) by 8 we have,
\begin{array}{rcl}
2C+2W=60.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
10C=140.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&140\div10\\
&=&14.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&30-14\\
&=&16.\tag{6}
\end{array}
Sophia attended a Australian Maths Trust (AMT). Sophia answered all 47 questions. For each correct answer, Sophia will get 4 marks. However, for each wrong answer, Sophia will be deducted by 2 mark(s). If Sophia scored 44 marks in total, how many questions did Sophia answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Sophia answered all the 47 questions correctly, and each correct answer has 4 marks, then Sophia should score 188 marks,
\begin{array}{rcl}
47\times4=188.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Sophia only scored 44 marks, therefore Sophia totally lost
\begin{array}{rcl}
188-44=144.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
144\div6=24.
\end{array}
The number of correct answers is
\begin{array}{rcl}
47-24=23.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 47, we have,
\begin{array}{rcl}
C+W=47.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=44.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=94.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=138.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&138\div6\\
&=&23.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&47-23\\
&=&24.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Sophia answered all the 47 questions correctly, and each correct answer has 4 marks, then Sophia should score 188 marks,
\begin{array}{rcl}
47\times4=188.
\end{array}
For every question Sophia answered wrongly, Sophia will lose,
\begin{array}{rcl}
4+2=6.
\end{array}
marks.
Since Sophia only scored 44 marks, therefore Sophia totally lost
\begin{array}{rcl}
188-44=144.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
144\div6=24.
\end{array}
The number of correct answers is
\begin{array}{rcl}
47-24=23.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 47, we have,
\begin{array}{rcl}
C+W=47.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
4C-2W=44.\tag{2}
\end{array}
Multiplying both sides of (1) by 4 we have,
\begin{array}{rcl}
2C+2W=94.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
6C=138.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&138\div6\\
&=&23.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&47-23\\
&=&24.\tag{6}
\end{array}
Emma attended a Australian Maths Trust (AMT). Emma answered all 48 questions. For each correct answer, Emma will get 4 marks. However, for each wrong answer, Emma will be deducted by 1 mark(s). If Emma scored 72 marks in total, how many questions did Emma answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Emma answered all the 48 questions correctly, and each correct answer has 4 marks, then Emma should score 192 marks,
\begin{array}{rcl}
48\times4=192.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Emma only scored 72 marks, therefore Emma totally lost
\begin{array}{rcl}
192-72=120.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
120\div5=24.
\end{array}
The number of correct answers is
\begin{array}{rcl}
48-24=24.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 48, we have,
\begin{array}{rcl}
C+W=48.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=72.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=120.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&120\div5\\
&=&24.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&48-24\\
&=&24.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Emma answered all the 48 questions correctly, and each correct answer has 4 marks, then Emma should score 192 marks,
\begin{array}{rcl}
48\times4=192.
\end{array}
For every question Emma answered wrongly, Emma will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Emma only scored 72 marks, therefore Emma totally lost
\begin{array}{rcl}
192-72=120.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
120\div5=24.
\end{array}
The number of correct answers is
\begin{array}{rcl}
48-24=24.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 48, we have,
\begin{array}{rcl}
C+W=48.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=72.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=120.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&120\div5\\
&=&24.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&48-24\\
&=&24.\tag{6}
\end{array}
Benjamin attended a Singapore Maths Olympaid (SMO). Benjamin answered all 33 questions. For each correct answer, Benjamin will get 5 marks. However, for each wrong answer, Benjamin will be deducted by 1 mark(s). If Benjamin scored 75 marks in total, how many questions did Benjamin answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Benjamin answered all the 33 questions correctly, and each correct answer has 5 marks, then Benjamin should score 165 marks,
\begin{array}{rcl}
33\times5=165.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Benjamin only scored 75 marks, therefore Benjamin totally lost
\begin{array}{rcl}
165-75=90.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
90\div6=15.
\end{array}
The number of correct answers is
\begin{array}{rcl}
33-15=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 33, we have,
\begin{array}{rcl}
C+W=33.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=75.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=108.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&108\div6\\
&=&18.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&33-18\\
&=&15.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Benjamin answered all the 33 questions correctly, and each correct answer has 5 marks, then Benjamin should score 165 marks,
\begin{array}{rcl}
33\times5=165.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Benjamin only scored 75 marks, therefore Benjamin totally lost
\begin{array}{rcl}
165-75=90.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
90\div6=15.
\end{array}
The number of correct answers is
\begin{array}{rcl}
33-15=18.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 33, we have,
\begin{array}{rcl}
C+W=33.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=75.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=108.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&108\div6\\
&=&18.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&33-18\\
&=&15.\tag{6}
\end{array}
Isabella attended a English Spelling Bee Competition. Isabella answered all 123 questions. For each correct answer, Isabella will get 10 marks. However, for each wrong answer, Isabella will be deducted by 2 mark(s). If Isabella scored 150 marks in total, how many questions did Isabella answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Isabella answered all the 123 questions correctly, and each correct answer has 10 marks, then Isabella should score 1230 marks,
\begin{array}{rcl}
123\times10=1230.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Isabella only scored 150 marks, therefore Isabella totally lost
\begin{array}{rcl}
1230-150=1080.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
1080\div12=90.
\end{array}
The number of correct answers is
\begin{array}{rcl}
123-90=33.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 123, we have,
\begin{array}{rcl}
C+W=123.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=150.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=246.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=396.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&396\div12\\
&=&33.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&123-33\\
&=&90.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Isabella answered all the 123 questions correctly, and each correct answer has 10 marks, then Isabella should score 1230 marks,
\begin{array}{rcl}
123\times10=1230.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Isabella only scored 150 marks, therefore Isabella totally lost
\begin{array}{rcl}
1230-150=1080.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
1080\div12=90.
\end{array}
The number of correct answers is
\begin{array}{rcl}
123-90=33.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 123, we have,
\begin{array}{rcl}
C+W=123.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=150.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=246.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=396.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&396\div12\\
&=&33.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&123-33\\
&=&90.\tag{6}
\end{array}
Isabella attended a Australian Maths Trust (AMT). Isabella answered all 37 questions. For each correct answer, Isabella will get 4 marks. However, for each wrong answer, Isabella will be deducted by 1 mark(s). If Isabella scored 48 marks in total, how many questions did Isabella answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Isabella answered all the 37 questions correctly, and each correct answer has 4 marks, then Isabella should score 148 marks,
\begin{array}{rcl}
37\times4=148.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Isabella only scored 48 marks, therefore Isabella totally lost
\begin{array}{rcl}
148-48=100.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
100\div5=20.
\end{array}
The number of correct answers is
\begin{array}{rcl}
37-20=17.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 37, we have,
\begin{array}{rcl}
C+W=37.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=48.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=85.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&85\div5\\
&=&17.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&37-17\\
&=&20.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Isabella answered all the 37 questions correctly, and each correct answer has 4 marks, then Isabella should score 148 marks,
\begin{array}{rcl}
37\times4=148.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Isabella only scored 48 marks, therefore Isabella totally lost
\begin{array}{rcl}
148-48=100.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
100\div5=20.
\end{array}
The number of correct answers is
\begin{array}{rcl}
37-20=17.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 37, we have,
\begin{array}{rcl}
C+W=37.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=48.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=85.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&85\div5\\
&=&17.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&37-17\\
&=&20.\tag{6}
\end{array}
Jacob attended a Maths Competition. Jacob answered all 43 questions. For each correct answer, Jacob will get 6 marks. However, for each wrong answer, Jacob will be deducted by 2 mark(s). If Jacob scored 66 marks in total, how many questions did Jacob answer wrongly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Jacob answered all the 43 questions correctly, and each correct answer has 6 marks, then Jacob should score 258 marks,
\begin{array}{rcl}
43\times6=258.
\end{array}
For every question Jacob answered wrongly, Jacob will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Jacob only scored 66 marks, therefore Jacob totally lost
\begin{array}{rcl}
258-66=192.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
192\div8=24.
\end{array}
The number of correct answers is
\begin{array}{rcl}
43-24=19.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 43, we have,
\begin{array}{rcl}
C+W=43.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=66.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=86.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=152.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&152\div8\\
&=&19.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&43-19\\
&=&24.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Jacob answered all the 43 questions correctly, and each correct answer has 6 marks, then Jacob should score 258 marks,
\begin{array}{rcl}
43\times6=258.
\end{array}
For every question Jacob answered wrongly, Jacob will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since Jacob only scored 66 marks, therefore Jacob totally lost
\begin{array}{rcl}
258-66=192.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
192\div8=24.
\end{array}
The number of correct answers is
\begin{array}{rcl}
43-24=19.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 43, we have,
\begin{array}{rcl}
C+W=43.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=66.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=86.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=152.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&152\div8\\
&=&19.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&43-19\\
&=&24.\tag{6}
\end{array}
Mason attended a American Maths Olympiad (AMO). Mason answered all 15 questions. For each correct answer, Mason will get 4 marks. However, for each wrong answer, Mason will be deducted by 1 mark(s). If Mason scored 60 marks in total, how many questions did Mason answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Mason answered all the 15 questions correctly, and each correct answer has 4 marks, then Mason should score 60 marks,
\begin{array}{rcl}
15\times4=60.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Mason only scored 60 marks, therefore Mason totally lost
\begin{array}{rcl}
60-60=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div5=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
15-0=15.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 15, we have,
\begin{array}{rcl}
C+W=15.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=60.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=75.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&75\div5\\
&=&15.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&15-15\\
&=&0.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Mason answered all the 15 questions correctly, and each correct answer has 4 marks, then Mason should score 60 marks,
\begin{array}{rcl}
15\times4=60.
\end{array}
For every question Mason answered wrongly, Mason will lose,
\begin{array}{rcl}
4+1=5.
\end{array}
marks.
Since Mason only scored 60 marks, therefore Mason totally lost
\begin{array}{rcl}
60-60=0.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
0\div5=0.
\end{array}
The number of correct answers is
\begin{array}{rcl}
15-0=15.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 15, we have,
\begin{array}{rcl}
C+W=15.\tag{1}
\end{array}
Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
4C-1W=60.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
5C=75.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&75\div5\\
&=&15.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&15-15\\
&=&0.\tag{6}
\end{array}
Isabella attended a Maths Competition. Isabella answered all 52 questions. For each correct answer, Isabella will get 10 marks. However, for each wrong answer, Isabella will be deducted by 2 mark(s). If Isabella scored 160 marks in total, how many questions did Isabella answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Isabella answered all the 52 questions correctly, and each correct answer has 10 marks, then Isabella should score 520 marks,
\begin{array}{rcl}
52\times10=520.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Isabella only scored 160 marks, therefore Isabella totally lost
\begin{array}{rcl}
520-160=360.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
360\div12=30.
\end{array}
The number of correct answers is
\begin{array}{rcl}
52-30=22.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 52, we have,
\begin{array}{rcl}
C+W=52.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=160.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=104.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=264.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&264\div12\\
&=&22.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&52-22\\
&=&30.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Isabella answered all the 52 questions correctly, and each correct answer has 10 marks, then Isabella should score 520 marks,
\begin{array}{rcl}
52\times10=520.
\end{array}
For every question Isabella answered wrongly, Isabella will lose,
\begin{array}{rcl}
10+2=12.
\end{array}
marks.
Since Isabella only scored 160 marks, therefore Isabella totally lost
\begin{array}{rcl}
520-160=360.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
360\div12=30.
\end{array}
The number of correct answers is
\begin{array}{rcl}
52-30=22.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 52, we have,
\begin{array}{rcl}
C+W=52.\tag{1}
\end{array}
Since for every correct answer gives 10 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
10C-2W=160.\tag{2}
\end{array}
Multiplying both sides of (1) by 10 we have,
\begin{array}{rcl}
2C+2W=104.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
12C=264.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&264\div12\\
&=&22.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&52-22\\
&=&30.\tag{6}
\end{array}
Benjamin attended a English Spelling Bee Competition. Benjamin answered all 73 questions. For each correct answer, Benjamin will get 5 marks. However, for each wrong answer, Benjamin will be deducted by 1 mark(s). If Benjamin scored 95 marks in total, how many questions did Benjamin answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume Benjamin answered all the 73 questions correctly, and each correct answer has 5 marks, then Benjamin should score 365 marks,
\begin{array}{rcl}
73\times5=365.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Benjamin only scored 95 marks, therefore Benjamin totally lost
\begin{array}{rcl}
365-95=270.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
270\div6=45.
\end{array}
The number of correct answers is
\begin{array}{rcl}
73-45=28.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 73, we have,
\begin{array}{rcl}
C+W=73.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=95.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=168.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&168\div6\\
&=&28.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&73-28\\
&=&45.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume Benjamin answered all the 73 questions correctly, and each correct answer has 5 marks, then Benjamin should score 365 marks,
\begin{array}{rcl}
73\times5=365.
\end{array}
For every question Benjamin answered wrongly, Benjamin will lose,
\begin{array}{rcl}
5+1=6.
\end{array}
marks.
Since Benjamin only scored 95 marks, therefore Benjamin totally lost
\begin{array}{rcl}
365-95=270.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
270\div6=45.
\end{array}
The number of correct answers is
\begin{array}{rcl}
73-45=28.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 73, we have,
\begin{array}{rcl}
C+W=73.\tag{1}
\end{array}
Since for every correct answer gives 5 marks, and every wrong aswer deducts 1 mark(s), the total score is,
\begin{array}{rcl}
5C-1W=95.\tag{2}
\end{array}
We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2),
\begin{array}{rcl}
6C=168.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&168\div6\\
&=&28.\tag{5}
\end{array}
From (4) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&73-28\\
&=&45.\tag{6}
\end{array}
James attended a Chinese Multiple Choices Test. James answered all 65 questions. For each correct answer, James will get 6 marks. However, for each wrong answer, James will be deducted by 2 mark(s). If James scored 102 marks in total, how many questions did James answer correctly?
Sorry. Please check the correct answer below.
Method 1: Method of Assumption
Assume James answered all the 65 questions correctly, and each correct answer has 6 marks, then James should score 390 marks,
\begin{array}{rcl}
65\times6=390.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since James only scored 102 marks, therefore James totally lost
\begin{array}{rcl}
390-102=288.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
288\div8=36.
\end{array}
The number of correct answers is
\begin{array}{rcl}
65-36=29.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 65, we have,
\begin{array}{rcl}
C+W=65.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=102.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=130.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=232.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&232\div8\\
&=&29.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&65-29\\
&=&36.\tag{6}
\end{array}
You are Right
Method 1: Method of Assumption
Assume James answered all the 65 questions correctly, and each correct answer has 6 marks, then James should score 390 marks,
\begin{array}{rcl}
65\times6=390.
\end{array}
For every question James answered wrongly, James will lose,
\begin{array}{rcl}
6+2=8.
\end{array}
marks.
Since James only scored 102 marks, therefore James totally lost
\begin{array}{rcl}
390-102=288.
\end{array}
marks due to the questions answered wrongly.
Therefore the number of wrong answers is
\begin{array}{rcl}
288\div8=36.
\end{array}
The number of correct answers is
\begin{array}{rcl}
65-36=29.
\end{array}
Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 65, we have,
\begin{array}{rcl}
C+W=65.\tag{1}
\end{array}
Since for every correct answer gives 6 marks, and every wrong aswer deducts 2 mark(s), the total score is,
\begin{array}{rcl}
6C-2W=102.\tag{2}
\end{array}
Multiplying both sides of (1) by 6 we have,
\begin{array}{rcl}
2C+2W=130.\tag{3}
\end{array}
We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3),
\begin{array}{rcl}
8C=232.\tag{4}
\end{array}
Therefore the number of correct answer is
\begin{array}{rcl}
C&=&232\div8\\
&=&29.\tag{5}
\end{array}
From (5) and (1) we have the number of wrong answer
\begin{array}{rcl}
W&=&65-29\\
&=&36.\tag{6}
\end{array}
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