cat 2022 Question 8

Question

The average of a non-decreasing sequence of N numbers $a_1, a_2, \ldots, a_N$ is 300 . If a_1 is replaced by $6a_1$ , the new average becomes 400. Then, the number of possible values of $a_1$ is

Accepted Answer

$a_1 + a_2 + ..... + a_N = 300_N$

$6_{a_1} + a_2 + ..... + a_N = 400_N$

$5_{a_1} = 100_N$

$a_1 = 20_N$

As the given sequence of numbers is non-decreasing sequence, N can take values from 2 to 15.

N is not equal to 1, if N = 1, then average of N numbers is 300 wouldn't satisfy.

Therefore, N can take values from 2 to 15, i.e. 14 values.

Question 8.

Question Explanation