2022 AMC 10A Problems/Problem 8
Problem
A data set consists of not distinct) positive integers: , , , , , and . The average (arithmetic mean) of the numbers equals a value in the data set. What is the sum of all positive values of ?
Solution
Case 1: the mean is
.
Case 2: the mean is
.
Case 3: the mean is
.
Hence, adding up the cases, the answer is .
~MrThinker