Bunuel wrote:

A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube?

A. 8p

B. pq

C. pq + 27

D. -p

E. (p - q)^6

A. since p is a perfect cube and 8 is a perfect cube, 8p will be a perfect cube. reject.

B. since p is a perfect cube and q is a perfect cube, pq will be a perfect cube. reject.

C. Hold.

D. since p is a perfect cube, -p will also be a perfect cube. reject.

E. (p-q)^6, is a perfect cube, so reject.

By elimination C is the answer.

Check say p = 1, q=8, then 8+27 = 35 --> not a perfect cube.