CAT 2022 Slot 1 QA Q7 Ratio, Mixtures & Averages

Question 7 of the Quantitative Ability (QA) section, CAT 2022 Slot 1, with CAT's official answer and a worked solution.

The average of three integers is 13 . When a natural number \(n\) is included, the average of these four integers remains an odd integer. The minimum possible value of \(n\) is
  1. A
    3
  2. B
    4
  3. C
    5
  4. D
    1

Answer: (C) 5 Ratio, Mixtures & Averages MCQ

Solution

  1. Sum of the three integers \(= 3 \times 13 = 39\).
  2. New average \(\frac{39 + n}{4}\) must be an odd integer, so \(39 + n = 4 \times \text{odd} \in \{44, 52, \dots\}\) (40 and 48 give even averages).
  3. Smallest: \(39 + n = 44 \Rightarrow n = 5\).

Shortcut. Try options in increasing order: \(n=1\) gives average 10 (even), \(n=3,4\) give non-integers, \(n=5\) gives 11.

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