CAT 2021 Slot 3 QA Q7 Ratio, Mixtures & Averages

Question 7 of the Quantitative Ability (QA) section, CAT 2021 Slot 3, with CAT's official answer and a worked solution.

The arithmetic mean of scores of 25 students in an examination is 50. Five of these students top the examination with the same score. If the scores of the other students are distinct integers with the lowest being 30, then the maximum possible score of the toppers is

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

Answer: 92 Ratio, Mixtures & Averages TITA

Solution

  1. Total score \(= 25 \times 50 = 1250\).
  2. To maximise the toppers' score, make the other 20 distinct integer scores as small as possible: \(30, 31, \dots, 49\), sum \(= 10 \times 79 = 790\).
  3. Toppers share \(1250 - 790 = 460\), so each scores \(\frac{460}{5} = 92\) (which is above 49, as needed).

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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