Question 1 of 10

Method 1: Method of Assumption
Assume William answered all the 38 questions correctly, and each correct answer has 2 marks, then William should score 76 marks, \begin{array}{rcl} 38\times2=76. \end{array} For every question William answered wrongly, William will lose, \begin{array}{rcl} 2+1=3. \end{array} marks.
Since William only scored 34 marks, therefore William totally lost \begin{array}{rcl} 76-34=42. \end{array} marks due to the questions answered wrongly.
Therefore the number of wrong answers is \begin{array}{rcl} 42\div3=14. \end{array} The number of correct answers is \begin{array}{rcl} 38-14=24. \end{array} Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 38, we have, \begin{array}{rcl} C+W=38.\tag{1} \end{array} Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is, \begin{array}{rcl} 2C-1W=34.\tag{2} \end{array} We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2), \begin{array}{rcl} 3C=72.\tag{4} \end{array} Therefore the number of correct answer is \begin{array}{rcl} C&=&72\div3\\ &=&24.\tag{5} \end{array} From (4) and (1) we have the number of wrong answer \begin{array}{rcl} W&=&38-24\\ &=&14.\tag{6} \end{array}

Method 1: Method of Assumption
Assume Noah answered all the 63 questions correctly, and each correct answer has 4 marks, then Noah should score 252 marks, \begin{array}{rcl} 63\times4=252. \end{array} For every question Noah answered wrongly, Noah will lose, \begin{array}{rcl} 4+2=6. \end{array} marks.
Since Noah only scored 60 marks, therefore Noah totally lost \begin{array}{rcl} 252-60=192. \end{array} marks due to the questions answered wrongly.
Therefore the number of wrong answers is \begin{array}{rcl} 192\div6=32. \end{array} The number of correct answers is \begin{array}{rcl} 63-32=31. \end{array} Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 63, we have, \begin{array}{rcl} C+W=63.\tag{1} \end{array} Since for every correct answer gives 4 marks, and every wrong aswer deducts 2 mark(s), the total score is, \begin{array}{rcl} 4C-2W=60.\tag{2} \end{array} Multiplying both sides of (1) by 4 we have, \begin{array}{rcl} 2C+2W=126.\tag{3} \end{array} We can eliminate $W$ by summing up the left side of (2) and (3), and also summing up the right side of (2) and (3), \begin{array}{rcl} 6C=186.\tag{4} \end{array} Therefore the number of correct answer is \begin{array}{rcl} C&=&186\div6\\ &=&31.\tag{5} \end{array} From (5) and (1) we have the number of wrong answer \begin{array}{rcl} W&=&63-31\\ &=&32.\tag{6} \end{array}

Method 1: Method of Assumption
Assume Noah answered all the 15 questions correctly, and each correct answer has 2 marks, then Noah should score 30 marks, \begin{array}{rcl} 15\times2=30. \end{array} For every question Noah answered wrongly, Noah will lose, \begin{array}{rcl} 2+1=3. \end{array} marks.
Since Noah only scored 30 marks, therefore Noah totally lost \begin{array}{rcl} 30-30=0. \end{array} marks due to the questions answered wrongly.
Therefore the number of wrong answers is \begin{array}{rcl} 0\div3=0. \end{array} The number of correct answers is \begin{array}{rcl} 15-0=15. \end{array} Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 15, we have, \begin{array}{rcl} C+W=15.\tag{1} \end{array} Since for every correct answer gives 2 marks, and every wrong aswer deducts 1 mark(s), the total score is, \begin{array}{rcl} 2C-1W=30.\tag{2} \end{array} We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2), \begin{array}{rcl} 3C=45.\tag{4} \end{array} Therefore the number of correct answer is \begin{array}{rcl} C&=&45\div3\\ &=&15.\tag{5} \end{array} From (4) and (1) we have the number of wrong answer \begin{array}{rcl} W&=&15-15\\ &=&0.\tag{6} \end{array}

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}

Method 1: Method of Assumption
Assume Mason answered all the 40 questions correctly, and each correct answer has 3 marks, then Mason should score 120 marks, \begin{array}{rcl} 40\times3=120. \end{array} For every question Mason answered wrongly, Mason will lose, \begin{array}{rcl} 3+1=4. \end{array} marks.
Since Mason only scored 48 marks, therefore Mason totally lost \begin{array}{rcl} 120-48=72. \end{array} marks due to the questions answered wrongly.
Therefore the number of wrong answers is \begin{array}{rcl} 72\div4=18. \end{array} The number of correct answers is \begin{array}{rcl} 40-18=22. \end{array} Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 40, we have, \begin{array}{rcl} C+W=40.\tag{1} \end{array} Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is, \begin{array}{rcl} 3C-1W=48.\tag{2} \end{array} We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2), \begin{array}{rcl} 4C=88.\tag{4} \end{array} Therefore the number of correct answer is \begin{array}{rcl} C&=&88\div4\\ &=&22.\tag{5} \end{array} From (4) and (1) we have the number of wrong answer \begin{array}{rcl} W&=&40-22\\ &=&18.\tag{6} \end{array}

Method 1: Method of Assumption
Assume William answered all the 40 questions correctly, and each correct answer has 3 marks, then William should score 120 marks, \begin{array}{rcl} 40\times3=120. \end{array} For every question William answered wrongly, William will lose, \begin{array}{rcl} 3+1=4. \end{array} marks.
Since William only scored 48 marks, therefore William totally lost \begin{array}{rcl} 120-48=72. \end{array} marks due to the questions answered wrongly.
Therefore the number of wrong answers is \begin{array}{rcl} 72\div4=18. \end{array} The number of correct answers is \begin{array}{rcl} 40-18=22. \end{array} Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 40, we have, \begin{array}{rcl} C+W=40.\tag{1} \end{array} Since for every correct answer gives 3 marks, and every wrong aswer deducts 1 mark(s), the total score is, \begin{array}{rcl} 3C-1W=48.\tag{2} \end{array} We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2), \begin{array}{rcl} 4C=88.\tag{4} \end{array} Therefore the number of correct answer is \begin{array}{rcl} C&=&88\div4\\ &=&22.\tag{5} \end{array} From (4) and (1) we have the number of wrong answer \begin{array}{rcl} W&=&40-22\\ &=&18.\tag{6} \end{array}

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}

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}

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}

Method 1: Method of Assumption
Assume Mason answered all the 36 questions correctly, and each correct answer has 4 marks, then Mason should score 144 marks, \begin{array}{rcl} 36\times4=144. \end{array} For every question Mason answered wrongly, Mason will lose, \begin{array}{rcl} 4+1=5. \end{array} marks.
Since Mason only scored 44 marks, therefore Mason totally lost \begin{array}{rcl} 144-44=100. \end{array} marks due to the questions answered wrongly.
Therefore the number of wrong answers is \begin{array}{rcl} 100\div5=20. \end{array} The number of correct answers is \begin{array}{rcl} 36-20=16. \end{array} Method 2: Simple Algebra
Let the number of correct answers be $C$, and the number of wrong answer be $W$.
Since the total number of questions is 36, we have, \begin{array}{rcl} C+W=36.\tag{1} \end{array} Since for every correct answer gives 4 marks, and every wrong aswer deducts 1 mark(s), the total score is, \begin{array}{rcl} 4C-1W=44.\tag{2} \end{array} We can eliminate $W$ by summing up the left side of (1) and (2), and also summing up the right side of (1) and (2), \begin{array}{rcl} 5C=80.\tag{4} \end{array} Therefore the number of correct answer is \begin{array}{rcl} C&=&80\div5\\ &=&16.\tag{5} \end{array} From (4) and (1) we have the number of wrong answer \begin{array}{rcl} W&=&36-16\\ &=&20.\tag{6} \end{array}