CAT 2022 Slot 3 QA Q5 Ratio, Mixtures & Averages

Question 5 of the Quantitative Ability (QA) section, CAT 2022 Slot 3, with CAT's official answer and a worked solution.

In an examination, the average marks of students in sections A and B are 32 and 60, respectively. The number of students in section A is 10 less than that in section B. If the average marks of all the students across both the sections combined is an integer, then the difference between the maximum and minimum possible number of students in section A is

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

Answer: 63 Ratio, Mixtures & Averages TITA

Solution

  1. Let section A have \(n\) students, B has \(n+10\).
  2. Combined average \(=\frac{32n+60(n+10)}{2n+10}=\frac{46n+300}{n+5}=46+\frac{70}{n+5}\).
  3. This is an integer when \(n+5\) divides 70; with \(n\ge1\), \(n+5\in\{7,10,14,35,70\}\), so \(n\in\{2,5,9,30,65\}\).
  4. Difference \(=65-2=63\).

Same concept in other years

See every question on Combined average of two groups from group sizes and averages.

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