Official Guide Explanation:
Problem Solving #148




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Solution and Metadata

Question: 148
Page: 173
Difficulty: 7 (Very Difficult)
Category 1: Arithmetic > Descriptive Statistics > Average
Category 2: Algebra > Simplifying Algebraic Expressions >

Explanation: To answer this question without a lot of trial and error requires recognizing that this is similar to a weighted average. Start by simplifying--multiply the numerators by 10 and 20, and add the fractions:

((10x + 20y)/(x + y))

This expression is the same as what would result from the question, "If each x cost $10 and each y cost $20, what was the average price of the x's and y's that Joe purchased?" The answer to that question would depend on the number of each item that Joe purchased, though given that both x and y are positive numbers, we would know that the weighted average is greater than 10 and less than 20. That eliminates (A) and (E).

We also know that y is greater than x. In other words, Joe purchased more of the $20 items than the $10 items. In that case, the weighted average must be closer to $20 than $10, so choice (D) is correct.

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