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25 December, 22:25

If the mean of 5 positive integers is 15, what is the maximum possible difference between the largest and the smallest of these 5 numbers?

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  1. 25 December, 22:53
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    if the 5 numbers are different, the maximum difference is 64

    Step-by-step explanation:

    We have 5 positive (different) integers, a, b, c, d and e (suppose that are ordered from least to largest, so a is the smallest and b is the largest.

    The mean will be:

    M = (a + b + c + d + e) / 5 = 15.

    Now, if we want to find the largest difference between a and e, then we must first select the first 4 numbers as the smallest numbers possible, this is:

    a = 1, b = 2, c = 3 and d = 4

    M = (1 + 2 + 3 + 4 + d) / 5 = 15

    M = (10 + d) / 5 = 15

    10 + d = 15*5 = 75

    d = 75 - 10 = 65

    then the difference between a and d is = 65 - 1 = 64.

    Now, if we take any of the first 4 numbers a little bit bigger, then we will see that the value of d must be smaller, and the difference between d and a will be smaller.
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