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## Official Guide Explanation:Data Sufficiency #127

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: 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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