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## Official Guide Explanation:Data Sufficiency #76

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

Question: 76
Page: 279
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Properties of Integers > Evens and Odds
Category 2: Arithmetic > Properties of Integers > Other

Explanation: In order for the product of three integers to be an even integer, at least one of the integers must be even.

Statement (1) is insufficient. It tells us that t is as much greater than p as p is greater than m. The three integers could be 3, 5, and 7, or 4, 14, and 24, just to name two examples. In the first case, the product is odd; in the second, the product is even.

Statement (2) is also insufficient. If t and m are 16 apart, they must either both be even or both be odd. If both are even, the product of the three integers is even. If both are odd (and p is odd as well), the product is odd.

Taken together, the statements are still insufficient. Since p is halfway between t and m (as given by (1)), t is 8 greater than p, and p is 8 greater than m. All three integers must either be even or odd. If all three are even, the product is even; if all three are odd, the product is odd. Choice (E) is correct.

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