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## Official Guide Explanation:Problem Solving #156

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: 156
Page: 174
Difficulty: 5 (Moderate)
Category 1: Word Problems > Mixture Problems >
Category 2: Arithmetic > Percents > other

Explanation: If the tank contains 10,000 gallons, 5% of which is sodium chloride, then 500 gallons are sodium chloride. If 2,500 gallons of water evaporate, that leaves 500 gallons of sodium chloride in a total of 7,500 gallons of solution. The percent is equivalent to the fraction (500/(7,500)) = (5/75) = (1/15). To quickly convert that to a percent, you could recognize that, since the denominator is a multiple of 3, it'll be a repeating decimal (such as 0.33 or 0.66) and select the only similar answer (choice (D)). Alternatively, you could set up a ratio: (1/15) = ((x)/100) and recognize that 15(7) = 105, just a little more than 100, so x is a little bit less than 7.

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