How many rectangular solids with integer edges have a volume of \(6\) cubic inches?

[Vincen]

How many rectangular solids with integer edges have a volume of \(6\) cubic inches?

A. \(> 1\)
B. \(> 2\)
C. \( > 3\)
D. \( > 4\)
E. \( > 6\)

Answer: B

Source: Economist

[Scott@TargetTestPrep]

How many rectangular solids with integer edges have a volume of \(6\) cubic inches?

A. \(> 1\)
B. \(> 2\)
C. \( > 3\)
D. \( > 4\)
E. \( > 6\)

Answer: B

Solution:

A rectangular solid with a volume of 6 cubic inches can have one of the following dimensions:

1 x 1 x 6,

1 x 2 x 3

Since the order of the dimensions doesn’t matter (for example, 1 x 6 x 1 is considered the same as 1 x 1 x 6), we see that there are only 2 possibilities.

(Note: The answer choices should not have a “greater than” sign.)

Answer: B