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## Official Guide Explanation:

Problem Solving #58

**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.

Click here for an example of the PDF booklets. Click here to purchase a PDF copy.

**Solution and Metadata**

**Question****: 58**

Page: 69

Difficulty: **4** (Moderately Easy)

Category 1: Arithmetic > Fractions >

Category 2: Arithmetic > Decimals >

**Explanation:** This is solvable via long division, but there's almost always a better way. Note that the numerator and denominator aren't that much different from 30 and 120, so the fraction is probably about (1/4). (If you only get that far, you can narrow the choices down to (A) and (B), a pretty good start.) However, you can do better. The equivalent of (1/4) with 31 in the numerator is (1/4)((31/31)) = (31/124). (31/125) has a slightly larger denominator, so it is equal to a slightly smaller number. The only answer choice that is slightly smaller than (1/4) is 0.248, choice (A).

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