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Quantitative Reasoning – Practice – Attempt carefully: there is a marking scheme!

PSA_LEVEL-UP_QNR3) A student is answering a multiple choice examination with 65 questions with a marking scheme as follow:
i) 1 mark for each correct answer,
ii) -1/4 for a wrong answer,
iii) -1/8 for a question that has not been attempted.

If the student gets 37 marks in the test then the least possible number of questions the student has not answered is:

A) 6
B) 5
C) 7
D) 4 

Ans:

Total number of questions= 65. Let ‘C’, ‘W’, ‘U’ be the number of correct answers, wrong answers and unattempted questions.

C + W + U = 65 —-(A)

C -W/4 – U/8 = 37
=> 8C -2W – U = 296 —–(B)

Multiplying (A) by 2 and adding to (B),

10C + U = 65*2 + 296 = 130 + 296 = 426

10C = 426 – U

From the above equation we must see that LHS is a multiple of 10, to make RHS as a multiple of 10 we must observe that U can be atleast 6.

10C= 426 – 6 = 420
=> C= 42, U =6, W = 17. Option A.

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