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A boy appeared in CAT for four consecutive year years, but coincidentally each time his net score was 75. He told me that there was $$\frac{1}{3}$$rd negative marking for every wrong answer and 1 mark was allotted for every correct answer. He has attempted all the questions every year, but certainly some answers have been wrong due conceptual problem. Which is not the total number of questions asked for CAT in any year, in that period?

A. 231

B. 163

C. 150

D. 123

E. None of these

Answer: Option C

Solution(By Examveda Team)

Option method:
The best way to go through options. You will find that when you consider 150 questions you cannot get 75 marks anyhow.

Alternatively:
Since 75 is an integer, he must have to do (75 + 4x) problems, where x is a whole number. Now we put the value of x (0, 1, 2, 3, 4, 5 .........) to get the correct answer.
As he gets the net marks in integer it means when he does 3n question wrong, he losses actually 4n marks.

This Question Belongs to Arithmetic Ability >> Number System

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