NIMCET 2026 — Reasoning PYQ

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Question

NIMCET 2026 — Reasoning PYQ

NIMCET | Reasoning | 2026

An examination consists of 160 questions. One mark is given for every correct option. If a 1/4 mark is deducted for each wrong option and a half mark is deducted for each unanswered question, then a student scores 79. If half a mark is deducted for every wrong option and 1/4 mark is deducted for every unanswered question, the person scores 76. Find the number of correct answers he wrote?

Choose the correct answer:

Explanation

To solve this problem, let $x$ be the number of correct answers, $y$ be the number of wrong answers, and $z$ be the number of unanswered questions.

Step 1: Set up the equations

The total number of questions is 160:
$x + y + z = 160$
From the first scoring scenario:
$x - 0.25 y - 0.5 z = 79$
From the second scoring scenario:
$x - 0.5 y - 0.25 z = 76$

Step 2: Simplify the system

From the first equation, $z = 160 - x - y$ . Substituting this into the scoring equations:

First equation: $x - 0.25 y - 0.5 (160 - x - y) = 79$
$x - 0.25 y - 80 + 0.5 x + 0.5 y = 79$
$1.5 x + 0.25 y = 159$ — (Equation A)
Second equation: $x - 0.5 y - 0.25 (160 - x - y) = 76$
$x - 0.5 y - 40 + 0.25 x + 0.25 y = 76$
$1.25 x - 0.25 y = 116$ — (Equation B)

Step 3: Solve for $x$

Adding Equation A and Equation B eliminates $y$ :

$(1.5 x + 0.25 y) + (1.25 x - 0.25 y) = 159 + 116$

$2.75 x = 275$

$x = \frac{275}{2.75} = 100$

Conclusion:

The number of correct answers written by the student is 100, which corresponds to option 2.