Question

Average of 5 integers is 38 and all the numbers are between 0 and 50 (both inclusive). In these 5 numbers, a is the minimum. If exactly 3 of them are more than 32, find the difference between the minimum and the maximum value of a.

Answer 1

Given, the average marks for all the students is \(38\).
Total marks \( = 5\times38=190\)
Maximum scores of remaining students \(= 50 +49 +48 + 32 = 179\)
Minimum possible score \(= 190 - 179 = 11\)
\(⇒\) Maximum possible score \(=31\)
The difference between the minimum and the maximum value of a \(= 31-11 = 20\)

So, the answer is \(20\).