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## Official Guide Explanation:

Problem Solving #8

**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.

Click here for an example of the PDF booklets. Click here to purchase a PDF copy.

**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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