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## Official Guide Explanation:

Problem Solving #178

**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.

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**Solution and Metadata**

**Question****: 178**

Page: 177

Difficulty: **6** (Moderately Difficult)

Category 1: Arithmetic > Sets > 3+ sets

Category 2: Word Problems > Sets >

**Explanation:** The total number of students listed in the chart is 40 + 30 + 25 = 95. However, some of those students are double - counted: those students who, for instance, are in both Chess and Drama were counted in each of those categories. To remedy that problem, we need to subtract the number of students who were in each pair of clubs. Since the question tells us that there were 10, 5, and 6 students in various pairs of clubs (and no students in all three), the actual number of students is given by 95 - 10 - 5 - 6 = 74, choice (C).

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