CAT 2022 Slot 2 QA Q15 Equations

Question 15 of the Quantitative Ability (QA) section, CAT 2022 Slot 2, with CAT's official answer and a worked solution.

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 total of 97 marks in the examination. If the number of unattempted questions was higher than the number of attempted questions, then the maximum number of correct answers that Rayan could have given in the examination is

TITA: type in the answer. There are no options and no negative marking.

Answer: 24 Equations TITA

Solution

  1. Let \(c,w,u\) be correct, wrong, unattempted: \(c+w+u=75\), \(3c-w+u=97\). Subtracting gives \(c-w=11\).
  2. \(u>c+w\) means \(c+w\le37\), so \(2w+11\le37\), \(w\le13\).
  3. Maximum \(c=13+11=24\) (with \(u=38\)): \(72-13+38=97\).

Same concept in other years

See every question on Integer solutions of a linear equation with count and range constraints.

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