Official Guide Explanation:
Data Sufficiency #127




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Solution and Metadata

Question: 127
Page: 284
Difficulty: 5 (Moderate)
Category 1: Word Problems > Sets >
Category 2: Arithmetic > Sets > 2 sets

Explanation: The total number of students at Jefferson School is given by 300 = S + F + B, where S is the number of students who study Spanish only, F is the number who study French only, and B is the number who study both. To find B, you'll need both F and S. Since any student among these 300 studies either one language or the other, if 100 do not study French, then 100 study Spanish only, so S = 100. Now only one more variable is required to solve for B.

Statement (1) provides that variable: if 60 do not study Spanish, those 60 must study French only, meaning that F = 60. With the values of S and F, you can solve for B. Statement (2) is also sufficient: if a total of 240 students study Spanish and 100 students study Spanish only, that leaves 140 students who study Spanish and study French. The correct choice is (D).

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