1973 AHSME Problem 31

In the following equation, each of the letters represents uniquely a different digit in base ten:

(YE) \cdot (ME) = TTT

The sum E+M+T+Y equals

\textbf{(A)}\ 19 \qquad \textbf{(B)}\ 20 \qquad \textbf{(C)}\ 21 \qquad \textbf{(D)}\ 22 \qquad \textbf{(E)}\ 24

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.