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## Official Guide Explanation:Data Sufficiency #126

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: 126
Page: 284
Difficulty: 5 (Moderate)
Category 1: Word Problems > Sets >
Category 2: Arithmetic > Sets > 2 sets

Explanation: Statement (1) is not sufficient: if 20 of the 60 cars had a stereo but no power windows, then 40 of the cars either had both, neither, or power windows but no stereo. Statement (2) is also not sufficient: if 30 of the 60 cars had both, that leaves 30 cars that either had stereo but no power windows, power windows but no stereo, or neither.

Taken together, it's still not enough information. Given what we know about 50 of the 60 cars, that leaves 10 cars that either have power windows but no stereo, or neither. Without knowing how many cars have power windows but not stereo, it's insufficient, choice (E).

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