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## Official Guide Explanation:Data Sufficiency #50

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.

Question: 50
Page: 277
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Sets > 2 sets
Category 2: Word Problems > Sets >

Explanation: Judging from the question, this looks like a question that involves overlapping sets: there will be some directors of Companies K and R that overlap and others who don't. Statement (1) is not sufficient, but it does provide some information: 17 = (K directors) + (R directors) - (directors in both K and R). Statement (2) is also insufficient, as it gives no indication how much overlap there is.

Taken together, the statements are sufficient. According to (1): 17 = (K directors) + (R directors) - (directors in both K and R). (2) fills in some of those gaps:

17 = 12 + 8 - overlap

17 = 20 - overlap

overlap = 3

Thus, the correct choice is (C).

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