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## Official Guide Explanation:Problem Solving #48

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: 48
Page: 68
Difficulty: 4 (Moderately Easy)
Category 1: Arithmetic > Fractions >

Explanation: First, recognize that (3/8) is less than (1/2), and three of the fractions are greater than (1/2). That means that our middle number will be the smallest of these three fractions, (9/16), (17/24), and (3/4). The quickest way to compare fractions like this is to find a common denominator, in this case 48 (which is divisible by 4, 16, and 24). Adjust the fractions as follows:

(9/16)((3/3)) = (27/48)

(17/24)((2/2)) = (34/48)

(3/4)((12/12)) = (36/48)

The smallest of these is (9/16), so that must be the middle number of the sequence. The correct choice is (E).

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