2000 AMC 10 Problem 23

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.