Question

Five positive integers have a mean of 8. What is the greatest possible value for the median of

the five integers?

Answer 1

12

Explanation:

Since there are 5 positive integers, and their mean is 8, then since 5 × 8 = 40, their sum must be 40.

We need to write 5 positive integers, in ascending order, whose sum is 40, and which have the greatest possible 3rd number.

For example,

8, 8, 8, 8, 8 has a sum of 40 and a median of 8.

6, 7, 9, 9, 9 has a sum of 40 and a median of 9.

We make the first two numbers as small as possible, so we can make the third number the greatest possible.

1, 1, 12, 13, 13

Answer: 12