2000 AMC 12 Problem 14

When the mean, median, and mode of the list

10,2,5,2,4,2,x

are arranged in increasing order, they form a non-constant arithmetic progression. What is the sum of all possible real values of x?

\textbf {(A)}\ 3 \qquad \textbf {(B)}\ 6 \qquad \textbf{(C)}\ 9 \qquad \textbf {(D)}\ 17 \qquad \textbf {(E)}\ 20

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.