UPSC CDS I 2025 Mathematics Paper

Given:
The average of 64,69,72,75,x lies between 62 and 76 (excluding 62 and 76).
Formula used:
‌ Average ‌=‌

‌ Sum of all numbers ‌

‌ Total numbers ‌

Calculation:
Let the sum of the given numbers =64+69+72+75+x=280+x
The average =‌

280+x

5

Since the average lies between 62 and 76:
‌⇒62<‌

280+x

5

<76
‌⇒310<280+x<380
‌⇒30<x<100
The possible integer values of x are from 31 to 99 (both inclusive).
Total number of integers =99−31+1=69