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## Official Guide Explanation:Problem Solving #8

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: 8
Page: 63
Difficulty: 3 (Very Easy)
Category 1: Arithmetic > Powers and Roots of Numbers > Roots
Category 2: Arithmetic > Fractions >

Explanation: A reciprocal is the inverse of a number: the reciprocal of x is (1/(x)). I is a pair of reciprocals. II is not: the reciprocal of (1/17) is 17. III is a pair of reciprocals. You might first write the reciprocal of rt[3] as (1/( rt[3])), but the GMAT almost never accepts radicals in the denominator of a fraction. To get rid of the radical, multiply the top and bottom by rt[3] as follows: ((1/( rt[3])))((( rt[3])/( rt[3]))) = ((( rt[3])/( rt[3] rt[3]))) = ((( rt[3])/3)), Thus, the answer is I and III, choice (D).

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