2000 Gauss 7 Problem 21

In a basketball shooting competition, each competitor shoots ten balls which are numbered from 1 to 10. The number of points earned for each successful shot is equal to the number on the ball. If a competitor misses exactly two shots, which one of the following scores is not possible?

\textbf{(A)}\ 52\quad \textbf{(B)}\ 44\quad \textbf{(C)}\ 41\quad \textbf{(D)}\ 38\quad \textbf{(E)}\ 35

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 Gauss contests here.