1965 AHSME Problem 5

When the repeating decimal 0.363636\ldots is written in simplest fractional form, the sum of the numerator and denominator is:

\textbf{(A)}\ 15 \qquad \textbf{(B) }\ 45 \qquad \textbf{(C) }\ 114 \qquad \textbf{(D) }\ 135 \qquad \textbf{(E) }\ 150

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