Official Guide Explanation:
Data Sufficiency #106

Background

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Solution and Metadata

Question: 106
Page: 282
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Properties of Integers > Factors and Multiples

Explanation: For the product of two integers to be even, at least one of the integers must be even.

Statement (1) is sufficient. If x is 1 greater than y, one of the numbers is odd and one is even. (We don't know which one, but it doesn't matter.) Since one of the numbers is even, the product is even.

Statement (2) is also sufficient. It's easier to understand this if you multiply both sides by y:

((x)/(y)) = even

x = even(y)

Any integer multiplied by an even is even, so even * y = even, so x is even. Since x is even, we know that the product of the two integers is even. Choice (D) is correct.

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