2021 JMPSC Accuracy Problems/Problem 2

Problem

Three distinct even positive integers are chosen between and inclusive. What is the largest possible average of these three integers?

Solution

The three biggest distinct positive integers that are or less are , , and . Thus, our answer is .

~Bradygho

Solution 2 (Quick and a good way to check your answer)

Notice that the average of numbers that form an arithmetic progression is the median of the numbers. Also, notice that to maximize the average of three numbers, we need to maximize the numbers themselves. Using these observations, it is obvious the answer is