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## Official Guide Explanation:Data Sufficiency #85

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: 85
Page: 159
Difficulty: 5 (Moderate)
Category 1: Word Problems > Sets >
Category 2: Arithmetic > Sets > 2 sets

Explanation: This is an overlapping sets question. Of the 30 businesses, 21 reported a profit and 15 had investments in foreign markets. We're looking for the number that did neither of those things. The other missing variable is how many did both of those things:

Total = Group1 + Group2 - Both + Neither

30 = 21 + 15 - Both + Neither

Statement (1) is sufficient. This gives us "Both," which leaves us with one variable in the equation above. We can solve for it.

Statement (2) is also sufficient. "1, 2, or both" is expressed like this:

Total = Group1 + Group2 - Both

24 = 21 + 15 - Both

Here we can solve for "Both," leaving us in the same position we were in with (1),able to solve for "Neither." Choice (D) is correct.

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