2017 Pascal Problem 23

An *Anderson number* is a positive integer k less than 10\,000 with the property that k^2 ends with the digit or digits of k. For example, 25 is an Anderson number because 625 ends with 25, but 75 is not an Anderson number because 5625 does not end with 75. If S is the sum of all *even* Anderson numbers, what is the sum of the digits of S?

\textbf{(A)}\ 17\quad \textbf{(B)}\ 18\quad \textbf{(C)}\ 11\quad \textbf{(D)}\ 33\quad \textbf{(E)}\ 24

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.