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Official Guide Explanation:Problem Solving #67

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.

Solution and Metadata

Question: 67
Page: 161
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Discrete Probability >

Explanation: There are a couple of ways to easily manage this problem. The traditional way is to recognize that there are four pairs of numbers that can be selected from the two sets that sum to 9. (Those are (2, 7), (3, 6), (4, 5), and (5, 4).) Probability is the number of desired outcomes over the number of possible outcomes, so we know the numerator: 4. The number of possible outcomes when selecting one number from each set is the product of the number of possible outcomes for each, or 4(5) = 20. Thus, the probability is (4/20) = (1/5) = 0.20, choice (B).

The alternative is to recognize that, no matter which number is chosen from set A, there is a 1 in 5 chance that the number chosen from set B will result in a sum of 9. In other words, there's a 100% chance of selecting a number from the first set that gives you a chance to have a sum of 9. Then, there's a 20% chance that the number selected from the second set will result in a total of exactly 9.

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