Official Guide Explanation:
Problem Solving #47




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Solution and Metadata

Question: 47
Page: 158
Difficulty: 4 (Moderately Easy)
Category 1: Arithmetic > Percents > other
Category 2: Word Problems > Mixture Problems >
Category 3: Word Problems > Rate Problems > other

Explanation: This problem can be solved by simply doing all of the calculations: finding 57% of 200, 42% of 300, and then dividing the total by 500. But it's more valuable to see this as a weighted average question. Essentially, there's a heavier weight on 42% than on 57%, and by solving the problem, you can find the weighted average of those two percents. Think of it like this: ((200(57) + 300(42))/500), which, as always, should be simplified: ((2(57) + 3(42))/5). Better yet, recognize that when solving for a weighted average, it doesn't matter what the actual numbers are, it matters the distance between the numbers. So, remembering that you'll have to add 42 to the answer, subtract 42 from each of the percents, as follows: ((2(15) + 3(0))/5) = (30/5) = 6. Add 42 again, and your answer is 48, choice (C). Like many "shortcuts," this may seem cumbersome at first, but once internalized, it will help you race through problems like this one faster than ever before.

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