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## Official Guide Explanation:Problem Solving #115

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: 115
Page: 168
Difficulty: 5 (Moderate)
Category 1: Algebra > Equations >
Category 2: Arithmetic > Percents > Percent Change
Category 3: Word Problems > Discount >

Explanation: There are several equations you can set up from this question; the key is to do so efficiently, which will come with practice. If Mary's income is 60 percent more than Tim's, m = 1.6t. If Tim's is 40 percent less than Juan's, t = 0.6j. Finally, another way of writing the question is to look for the value of x in m = (((x)/100))j. You'll need to get m and j in the same equation, so look for a way to combine the first two. If you substitute 0.6j for t in the first equation, you're left with m = 1.6(0.6j) = 0.96j. Putting this equation together with m = (((x)/100))j, it's evident that x = 96, choice (C).

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