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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 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: 14
Page: 63
Difficulty: 4 (Moderately Easy)
Category 1: Arithmetic > Fractions >

Explanation: There are a number of handy ways to compare fractions. The typical way is to find a common denominator, which is easiest on this problem for choice (D). To compare (2/3) and (13/27), convert (2/3) to ((2(9))/(3(9))) = (18/27). (2/3) is bigger, so eliminate (D).

More powerful methods rely on comparing numbers with consecutive denominators and/or numerators. For instance, to compare (2/3) to (33/50), convert (2/3) to something nearby, like ((2(17))/(3(17))) = (34/51). If you add one to the numerator and denominator of a fraction, it gets bigger, so (34/51) > (33/50). Eliminate (A).

You can analyze (B) in a similar way. Convert (2/3) to ((2(4))/(3(4))) = (8/12). If two fractions have the same numerator, the one with the smaller denominator is the bigger number, so (8/11) > (8/12), so (B) is the choice that is larger than (2/3).

For the sake of completeness, let's compare (C) and (E) to (2/3), as well. (2/3) = (4/6), and (4/6) > (3/5), so (C) is smaller than (2/3). Similarly, (2/3) = (6/9), and (6/9) > (5/8), so (E) is smaller, as well.

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