2010 Cayley Problem 11

If x and y are positive integers with x + y = 31, then the largest possible value of xy is

\textbf{(A)}\ 240\quad \textbf{(B)}\ 238\quad \textbf{(C)}\ 255\quad \textbf{(D)}\ 248\quad \textbf{(E)}\ 242

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 Cayley contests here.