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Mean and Median Mystery (Posted on 2025-01-08)

Find the sum of all positive integers n where the mean and median of {20, 42, 69, n} are both integers.

No Solution Yet Submitted by Danish Ahmed Khan

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Solution

Comment 2 of 2 |

For the mean to be an integer, n must be odd.

Since the sum 20 + 42 + 69 = 131 which is 3 mod 4,

n must be 1 mod 4.

If n < 20, the median is 31, check.

If n > 20, and n is odd, the median will not be an integer.

So n can be any integer less than 20 and 1 mod 4: {1,5,9,13,17}

the sum of which is 45.

Posted by Larry on 2025-01-08 11:28:30

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