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## Official Guide Explanation:

Problem Solving #79

**Background**

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd 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.

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**Solution and Metadata**

**Question****: 79**

Page: 72

Difficulty: **6** (Moderately Difficult)

Category 1: Arithmetic > Properties of Integers > Evens and Odds

Category 2: Arithmetic > Discrete Probability >

**Explanation:** When two integers are multiplied together, the result is even if one or both of the integers is even. In this case, we want the probability that the result is even; rather than finding the probability that one * * both is even, it's easier to find the probability that the result is odd. For the result to be odd, both integers must be odd. The probability of two indepedent events occuring is (p_{1})(p_{2}), so the probability of the result being odd is the probability of the first integer being odd times the probability of the second integer being odd.

Since two of the four numbers in the first set are odd, the probability of the first integer being odd is (2/4) = (1/2). The second set has two odd numbers out of a total of three, so the probability that the second number is odd is (2/3). The probability of the result being odd, then, is ((1/2))((2/3)) = (1/3). However, we're interested in the probability that the result is even, so we have to subtract the probability that it's odd from 1: 1 - (1/3) = (2/3), choice (D).

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