1991 AHSME Problem 28

Initially an urn contains 100 white and 100 black marbles. Repeatedly 3 marbles are removed (at random) from the urn and replaced with some marbles from a pile outside the urn as follows: 3 blacks are replaced with 1 black, or 2 blacks and 1 white are replaced with a white and a black, or 1 black and 2 whites are replaced with 2 whites, or 3 whites are replaced with a black and a white. Which of the following could be the contents of the urn after repeated applications of this procedure?

\textbf{(A) } 2 black \qquad \textbf{(B) } 2 white \qquad \textbf{(C) } 1 black \qquad \textbf{(D) } 1 black and 1 white \qquad \textbf{(E) } 1 white

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