Problem:
One dimension of a cube is increased by , another is decreased by , and the third is left unchanged. The volume of the new rectangular solid is less than that of the cube. What was the volume of the cube?
Answer Choices:
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Solution:
Let be the side length of the cube. Then the volume of the cube was , and the volume of the new solid is . Therefore , from which , and the volume of the cube was .
The problems on this page are the property of the MAA's American Mathematics Competitions