2007 Fermat Problem 15

How many three-digit positive integers x are there with the property that x and 2x have only even digits? (One such number is x = 420, since 2x = 840 and each of x and 2x has only even digits.)

\textbf{(A)}\ 64\quad \textbf{(B)}\ 18\quad \textbf{(C)}\ 16\quad \textbf{(D)}\ 125\quad \textbf{(E)}\ 100

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