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Question 1 of 190
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}
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.
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}
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}
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}
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}
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}
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}
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}
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}
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}
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 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}
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}
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 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}
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}
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}
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}
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 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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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.
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}
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}
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}
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}
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}
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 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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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 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}
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}
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 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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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?