If the average of five distinct positive integers is 10, what is the difference between the largest and the least possible values of the greatest of the five integers?

Explanation: The average of 5 distinct positive integer is 10 , so their sum must be \(10\times5=50\). In order to find the greatest possible value of the largest integer, we take 4 integers to be the minimum possible values. That gives us, 1, 2, 3 and 4 . So the greatest possible value for the largest number is \(50 - (1+2+3+4) = 40\). The smallest possible value of the largest integer can be found if we take consecutive integers, keeping 10 (average) in the middle. The series is, \(8, 9, 10, 11, 12\). So the smallest possible value of the greatest integer is 12. \(40-12=28\).