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## Official Guide Explanation:Problem Solving #18

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.

Question: 18
Page: 64
Difficulty: 5 (Moderate)
Category 1: Word Problems > Sets >
Category 2: Arithmetic > Sets > 2 sets

Explanation: The trickiest part of this question is understanding what they're asking you. X Δ Y is the number of integers in the sets that is not in both. First, find the total number of integers in the sets. If there are 10 in X, 18 in Y, and 6 in both, that's a total of 10 + 18 - 6 = 22 integers. (The six that are in both are counted in both X's total and Y's total, so must be subtracted from the sum of the two sets.) To find X Δ Y, subtract the number of integers in both from the total number of integers: 22 - 6 = 16, choice (B).

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