CAT 2020 Slot 3 QA Question & Solution
AlgebraMedium
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
Options
4
3
2
1
Solution
Given, $\frac{\text{sum of scores in n matches+38+15}}{n+2}=29$
Given, $\frac{\text{sum of scores in n matches}}{n}=30$
=> 30n + 53 = 29(n+2) => n=5
Sum of the scores in 5 matches = 29*7 - 38-15 = 150
Since the batsmen scored less than 38, in each of the first 5 innings. The value of x will be minimum when remaining four values are highest
=> 37+37+37+37 + x = 150
=> x = 2