CAT 2024 Slot 3 QA Q13 Ratio, Mixtures & Averages

Question 13 of the Quantitative Ability (QA) section, CAT 2024 Slot 3, with CAT's official answer and a worked solution.

The average of three distinct real numbers is 28. If the smallest number is increased by 7 and the largest number is reduced by 10, the order of the numbers remains unchanged, and the new arithmetic mean becomes 2 more than the middle number, while the difference between the largest and the smallest numbers becomes 64. Then, the largest number in the original set of three numbers is

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

Answer: 70 Ratio, Mixtures & Averages TITA

Solution

  1. Let \(a < b < c\), \(a + b + c = 84\).
  2. New numbers \(a+7, b, c-10\) have mean \(\frac{81}{3} = 27 = b + 2\), so \(b = 25\) and \(a + c = 59\).
  3. \((c - 10) - (a + 7) = 64 \Rightarrow c - a = 81\). So \(c = 70\).

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