Official Guide Explanation:
Problem Solving #8




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Solution and Metadata

Question: 8
Page: 153
Difficulty: 4 (Moderately Easy)
Category 1: Word Problems > Rate Problems > other
Category 2: Arithmetic > Ratio and Proportion >
Category 3: Arithmetic > Percents > other

Explanation: If the storm increased the amount of water to 138 billion gallons, and that amount of 82 percent of total capacity, we can write as follows: 0.82c = 138. To find the answer, the difference between the original amount of water (124 billion gallons) and capacity, we'll need to solve for c. By dividing each side by 0.82, we can see that c = (138/(0.82)), but that doesn't look like a very appealing calculation. Instead, approximate (the question, after all, is looking for an approximate number). If you round each number to (140/(0.8)), you have a much easier problem--just remember that by increasing the numerator and decreasing the denominator, you'll come up with a value for c that is too large. (140/(0.8)) = (1400/8) = 175, and 175 - 124 = 51, which should be higher than the correct answer. The only choice in the ballpark of 51 is 44, choice (E), which, as we anticipated, is lower than our rough approximation.

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