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smc

prealgebra senior

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 possible values of ?
(A)
(B)
(C)
(D)
Solution
First, note that . There are possible cases: Case 1: the mean is . . Case 2: the mean is . . Case 3: the mean is . . Therefore, the answer is .
Final answer
D