Official Guide Explanation:
Data Sufficiency #85

Background

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Solution and Metadata

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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