Official Guide Explanation:
Data Sufficiency #59

Background

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Solution and Metadata

Question: 59
Page: 278
Difficulty: 4 (Moderately Easy)
Category 1: Word Problems > Mixture Problems >
Category 2: Arithmetic > Fractions >

Explanation: Statement (1) is insufficient. We don't know how many students are in section 1 (which would tell us how many students (2/3) represents), and we don't know how many female students are in section 2.

Statement (2) is also insufficient. As with (1), we don't know the size of the given section, nor do we know anything about the other section.

Taken together, the statements are still insufficient. This is essentially a weighted average question. Since (2/3) of the students in one section are female and (1/2) of the students in the other section are female, the number of female students must be between the two fractions. But unless we know how many students are in each section, we don't know where the weighted average falls in between those two fractions. Choice (E) is correct.

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