Official Guide Explanation:
Data Sufficiency #21

Background

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Solution and Metadata

Question: 21
Page: 274
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Percents > other
Category 2: Arithmetic > Sets > 2 sets
Category 3: Word Problems > Sets >

Explanation: We're looking for the percentage of drama club members who are female.

Statement (1) is insufficient. 40 percent of the female students are members of the drama club, but those 40 percent could represent all of the drama club members (e.g., there are no men in drama club), or a much smaller percentage (if there are many men in drama club).

Statement (2) is also insufficient. 25 percent of men are members of the drama club, but by the same reasoning as the previous statement, we don't know what percentage of drama club members those 25 percent of men occupy.

Taken together, the statements are still insufficient. If we knew there were exactly 100 men and 100 women at the school (for instance--any equal number will do), we could determine how many men and women (25 and 40) are in drama club and answer the question. However, we don't know that the number of men and women are equal. If there 200 men and 100 women, the number in drama club is 50 and 40, changing the percentages drastically. Choice (E) is correct.

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