Problem:
A rectangular box has integer side lengths in the ratio . Which of the following could be the volume of the box?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let the dimensions of the box be , and . Then the volume of the box is . Therefore the volume must be times the cube of an integer. Among the choices, only , and are multiples of , and only for is the other factor a perfect cube.
The problems on this page are the property of the MAA's American Mathematics Competitions