CAT 2020 Quant Question [Slot 3] with Solution 24

Question

A batsman played n + 2 innings and got out on all occasions. His average score in these n + 2 innings was 29 runs and he scored 38 and 15 runs in the last two innings. The batsman scored less than 38 runs in each of the first n innings. In these n innings, his average score was 30 runs and lowest score was x runs. The smallest possible value of x is

  1. 2
  2. 3
  3. 4
  4. 1
Option: 1
Solution:

Total score in \((n + 2)\) innings \( = 29 \times (n + 2)\)

The total score in \(n\) innings \( = 29(n + 2) - 38 - 15\)

\( = 29n + 5 = 30n \Rightarrow n = 5\)

Total score in 5 innings \( = 30 \times 5 = 150 = 37 \times 4 + 2\)

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