A box contains 105 black balls, 89 gray balls, and 5 white balls. Outside the box, there are white balls in sufficient quantity to repeatedly perform the following procedure until only two balls remain in the box:

- two balls are removed from the box without looking;
- if the balls removed are of different colors, the darker one is returned to the box;
- otherwise, the balls removed are discarded, and a white ball is placed in the box.

Regarding the colors of the two remaining balls, it can be guaranteed that:

A) both will be white.

B) both will be gray.

C) both will be black.

D) exactly one will be black.

E) exactly one will be gray.
Solution

## ALTERNATIVE D

When two black balls are removed from the box, they do not return; but when the balls removed are one black and one of a different color, the black one returns. This shows that the number of black balls in the box decreases by two at a time. Since the initial number of black balls is odd, there will always be an odd number of black balls in the box; thus, exactly one of the two balls that remain in the box is black.