2006 Gauss 8 Problem 20

In the addition of two 2-digit numbers, each blank space, including those in the answer, is to be filled with one of the digits 0, 1, 2, 3, 4, 5, 6, each used exactly once. The units digit of the sum is

\begin{array}{cccc} & & \square & \square \\ + & & \square & \square \\ \hline & \square & \square & ? \end{array}

\textbf{(A)}\ 2\quad \textbf{(B)}\ 3\quad \textbf{(C)}\ 4\quad \textbf{(D)}\ 5\quad \textbf{(E)}\ 6

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.