CAT 2022 Slot 2 QA Q16 Inequalities & Modulus

Question 16 of the Quantitative Ability (QA) section, CAT 2022 Slot 2, with CAT's official answer and a worked solution.

Five students, including Amit, appear for an examination in which possible marks are integers between 0 and 50, both inclusive. The average marks for all the students is 38 and exactly three students got more than 32. If no two students got the same marks and Amit got the least marks among the five students, then the difference between the highest and lowest possible marks of Amit is
  1. A
    21
  2. B
    24
  3. C
    20
  4. D
    22

Answer: (C) 20 Inequalities & Modulus MCQ

Solution

  1. The total is \(5\times38=190\). Three students score above 32; Amit and one other score at most 32.
  2. Max for Amit: the other low scorer gets 32 and Amit 31; the top three need 127, e.g. 40, 43, 44. So the max is 31.
  3. Min for Amit: top three 50, 49, 48 (147) and the other 32, so Amit \(=190-179=11\).
  4. Difference \(=31-11=20\).

Same concept in other years

See every question on Maximise or minimise one value given an average and distinct/bounded others.

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