Question

At the exam were 35 questions. With each question, there are four suggested answers of which only one is correct. For every correct answer, a person gets 5 points. If the question isn't answered person loses 1 point, and if it's incorrect person loses 2 points. Ann, Mary, Steve, John and Peter claim that they have 153, 167, 149, 169 and 173 points, respectively. Who is telling the truth?​

Answer 1

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Peter

Step-by-step explanation:

Ann has 153.

Mary has 167.

Steve has 149.

John has 169.

Peter has 173.

So, write it in increasing order.

149 < 153 < 167 < 169 < 173

Hence,

Steve < Ann < Mary < John < Peter

So, Peter has the most points and is telling the truth.

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Answer 2

Given: At the exam were 35 questions. With each question, there are four suggested answers of which only one is correct. For every correct answer, a person gets 5 points. If the question isn't answered person loses 1 point, and if it's incorrect person loses 2 points. Ann, Mary, Steve, John and Peter claim that they have 153, 167, 149, 169 and 173 points, respectively.

To find: The person who is telling the truth.

Solution:

According to the question, there are 35 questions and each correct answer gets 5 points. If a person marks the correct answer for all 35 questions, they would get a total of 175 mark. Thus, 175 is the maximum marks that a person can attain in the exam.

A person loses 1 point for an unanswered question and each answer carries five points so they lose a sum of 6 points. Similarly, if a person loses 2 points for an incorrect answer, they lose a sum of 7 points. Hence, the total marks lost by a person must be calculated in multiples of 6 or 7 or both.  

Steve has lost 26 marks (175-149) and that can be written as multiples of 6 and 7.

$26 = 2(6) + 2(7)$

John has lost 6 marks (175-169) which is a multiple of 6. The others, that are Ann, Mary and Peter have lost marks which cannot be written in multiples of 6 or 7 or both.

Therefore, Steve and John are telling the truth.