CSAT Solved Papers/ 2021/Q58

2021 CSAT — Q58

Quant Arithmetic & numeracy 2.5 marks Easy

In an objective type test of $90$ questions, $5$ marks are allotted for every correct answer and $2$ marks are deducted for every wrong answer. After attempting all the $90$ questions, a student got a total of $387$ marks. What is the number of incorrect responses?

A 9 Answer
B 13
C 27
D 43

Worked rationale

Let $c$ be correct and $w = 90 - c$ be wrong (all attempted). Then

5c - 2(90 - c) = 387 \;\Rightarrow\; 5c - 180 + 2c = 387 \;\Rightarrow\; 7c = 567 \;\Rightarrow\; c = 81.

So wrong $= 90 - 81 = 9$ .

Answer: (a) 9.

Why the other options miss

B

an arithmetic slip: arithmetic error in $7c = 567$ (e.g. $7c = 561$ ), giving the wrong $c$ .
C

wrong formula: ignores the deduction (solves $5c = 387 + \dots$ wrongly) so the wrong-count comes out inflated.
D

answered the wrong quantity: sets up the score as $5c - 2w$ with $w$ as the unknown but solves for $c$ and reports it, or swaps correct/wrong.

Specialist insight

Negative-marking score problems are one linear equation once you use the “all attempted” link $w = 90 - c$ . Substituting collapses two unknowns to one: $7c = 567$ . The single trap is the deduction’s sign — each wrong answer costs $2$ , so the $-2(90-c)$ term adds $2c$ back, turning the coefficient into $7$ , not $5$ . Solve for $c$ , then the question wants $w = 9$ , so don’t stop at $c = 81$ .

The trap, in one line

$5c - 2(90-c) = 387 \Rightarrow 7c = 567 \Rightarrow c = 81$ , so wrong $= 9 \Rightarrow$ (a).

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