Official Guide Explanation:
Problem Solving #156




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Solution and Metadata

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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