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Official Guide Explanation:Problem Solving #14

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: 14
Page: 154
Difficulty: 5 (Moderate)
Category 1: Word Problems > Mixture Problems >
Category 2: Arithmetic > Descriptive Statistics > Average
Category 3: Arithmetic > Fractions >

Explanation: Weighted average problems can almost always be simplified. With that in mind, set up the question in algebraic terms, but don't do any calculations until you absolutely must. The weighted average formula for this question looks like this: ((8(12(3/8)) + 4(15(1/4)))/12). Since the denominator and each of the coefficients in the numerator are divisible by 4, simplify as follows: ((2(12(3/8)) + 1(15(1/4)))/3). There's still a bit of work involved, but that's much easier. 2(12(3/8)) = 24(3/4), and 24(3/4) + 15(1/4) = 40. Thus, the final answer will be equivalent to (40/3): it's choice (A), 13(1/3).

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