Official Guide Explanation:
Data Sufficiency #89

Background

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Solution and Metadata

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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