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Official Guide Explanation:Problem Solving #181

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: 181
Page: 178
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Fractions >
Category 2: Word Problems > Rate Problems > other

Explanation: With the first stroke, (1/2) of the original amount of air is removed, leaving (1/2). The second stroke, which removes half of what remains, eliminates (1/2)((1/2)) = (1/4), leaving (1/2) - (1/4) = (1/4). The third stroke eliminates (1/2)((1/4)) = (1/8), leaving (1/4) - (1/8) = (1/8). The fourth and final stroke eliminates (1/2)((1/8)) = (1/16), leaving (1/8) - (1/16) = (1/16). Since only (1/16) of the original amount of air remains, the total amount removed must be equal to 1 - (1/16) = (15/16), choice (A).

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