1993 AHSME Problem 7

The symbol R_k stands for an integer whose base-ten representation is a sequence of k ones. For example, R_3=111,R_5=11111, etc. When R_{24} is divided by R_4, the quotient Q=R_{24}/R_4 is an integer whose base-ten representation is a sequence containing only ones and zeroes. The number of zeros in Q is:

\text{(A) } 10\quad \text{(B) } 11\quad \text{(C) } 12\quad \text{(D) } 13\quad \text{(E) } 15

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