GRE Quantitative Practice, Complex Multiple-Choice
If p is a multiple of 3, which of the following expressions must in all cases represent a multiple of 2?
Indicate all such expressions.
C. p + 2
D. 3p + 1
The product of 2 and any positive integer is always a multiple of 2, and so (A) is a correct choice. Any odd integer multiplied by itself any number of times yields an odd integer, which of course cannot be a multiple of 2, hence (B) is an incorrect choice. The expression in (C) represents a multiple of 2 only when p is even. Conversely, the expression in (D) represents a multiple of 2 only when p is odd.
The correct answer is (A) only. You would gain credit for answering the question correctly by selecting this and only this one choice.