Official Guide Explanation:
Problem Solving #31

Background

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Solution and Metadata

Question: 31
Page: 65
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Properties of Integers > Evens and Odds

Explanation: Knowing that both x and y are not both odd isn't much: they could both be even, or one could be even and one odd. We'll have to go through each choice to find the answer:

(A): if both numbers are even, xy is even. If one is even and one odd, xy is also even. Thus, (A) is the correct answer.

(B): if both are even, x + y is even. If one is even and one odd, x + y is odd.

(C): if both are even, x - y is even. If one is even and one odd, x - y is odd.

(D): if both are even, x + y - 1 is odd. If one is even and one odd, x + y - 1 is even.

(E): No matter what x + y is, 2(x + y) is even. Thus, 2(x + y) - 1 is odd.

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