Official Guide Explanation:
Problem Solving #181




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Solution and Metadata

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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