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## Official Guide Explanation:Data Sufficiency #89

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: 89
Page: 280
Difficulty: 6 (Moderately Difficult)
Category 1: Word Problems > Sets >
Category 2: Arithmetic > Sets > 2 sets
Category 3: Arithmetic > Percents > other

Explanation: We're looking to compare two numbers: x (the number of members of Club X) and y (the number of members of Club Y).

Statement (1) is insufficient. 0.2x (20 percent of x) are also members of Club Y--let's call the overlapping group b. Thus:

0.2x = b

That doesn't tell us anything about how the two variables in the question compare.

Statement (2) is also insufficient. It gives us the same limited information about y:

0.3y = b

Taken together, the statements are sufficient. We can express both x and y in terms of b--the number of people in both clubs:

x = 5b

y = (10/3)b

5 is greater than (10/3), meaning that 5b is greater than (10/3)b, so x is greater than y. Choice (C) is correct.

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