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## Official Guide Explanation:

Data Sufficiency #76

**Background**

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**Solution and Metadata**

**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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