CAT 2022 Slot 2 QA Question 7: In an examination, there were 75 questions. 3 marks were awarded for each correct answer, 1 mark was deducted for each wrong answer and 1 mark was awarded for each unattempted question. Rayan scored a

Question

In an examination, there were 75 questions. 3 marks were awarded for each correct answer, 1 mark was deducted for each wrong answer and 1 mark was awarded for each unattempted question. Rayan scored a

Accepted Answer

Let the number of correct, wrong and unattempted questions be $c$, $w$ and $u$ respectively.

$c + w + u = 75$
$3c - w + u = 97$

Subtracting the first equation from the second:

$2c - 2w = 22$
$c - w = 11$
$c = w + 11$

The number of attempted questions is $c + w$. Since $u$ is higher than the numb