1958 AHSME Problem 28

A 16-quart radiator is filled with water. Four quarts are removed and replaced with pure antifreeze liquid. Then four quarts of the mixture are removed and replaced with pure antifreeze. This is done a third and a fourth time. The fractional part of the final mixture that is water is:

\textbf{(A)}\ \frac{1}{4}\qquad \textbf{(B)}\ \frac{81}{256}\qquad \textbf{(C)}\ \frac{27}{64}\qquad \textbf{(D)}\ \frac{37}{64}\qquad \textbf{(E)}\ \frac{175}{256}

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