1975 AHSME Problem 18

A positive integer N with three digits in its base ten representation is chosen at random, with each three digit number having an equal chance of being chosen. The probability that \log_2 N is an integer is

\textbf{(A)}\ 0 \qquad \textbf{(B)}\ 3/899 \qquad \textbf{(C)}\ 1/225 \qquad \textbf{(D)}\ 1/300 \qquad \textbf{(E)}\ 1/450

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