Integer problem discussed during today's Quant drill

Quantity A = remainder of (x^3 - x) / 6

Quantity B = remainder of (x^3 - x) / 8

If I take x=12, then quantity A becomes 0 and quantity B becomes 4. However @gregmat has told us that both quantities will be always zero and equal. I want to know the correct answer.

Is this the whole problem? Because if no other information is given, then the answer is indeed (D). If Greg said that it was (C), I believe there is some other piece of information that is missing on this post.

The answer is C.

Are you allowed to choose even numbers? You left some information out.