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## Official Guide Explanation:Problem Solving #176

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd 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: 176
Page: 85
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Fractions >

Explanation: Convert the mixed numbers to improper fractions, combine the resulting fractions in the numerator and denominator, and then divide by the fraction in the denominator. The process looks like this:

((2(3/5) - 1(2/3))/((2/3) - (3/5))) = (((13/5) - (5/3))/((2/3) - (3/5))) = ((((3(13))/15) - ((5(5))/15))/(((5(2))/15) - ((3(3))/15))) = (((39/15) - (25/15))/((10/15) - (9/15))) = ((((39 - 25)/15))/(((10 - 9)/15))) = (((14/15))/((1/15))) = ((14/15))((15/1)) = (14/1) = 14, choice (B).

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