1960 AHSME Problem 16

In the numeration system with base 5, counting is as follows: 1, 2, 3, 4, 10, 11, 12, 13, 14, 20,\ldots. The number whose description in the decimal system is 69, when described in the base 5 system, is a number with:

\begin{array}{l} \textbf{(A)}\ \text{two consecutive digits} \qquad\textbf{(B)}\ \text{two non-consecutive digits} \qquad \\ \textbf{(C)}\ \text{three consecutive digits} \qquad\textbf{(D)}\ \text{three non-consecutive digits} \qquad \\ \textbf{(E)}\ \text{four digits} \end{array}

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