2012 Pascal Problem 20

When the three-digit positive integer N is divided by 10, 11 or 12, the remainder is 7. What is the sum of the digits of N?

\textbf{(A)}\ 15\quad \textbf{(B)}\ 17\quad \textbf{(C)}\ 23\quad \textbf{(D)}\ 11\quad \textbf{(E)}\ 19

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.