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## Official Guide Explanation:Problem Solving #117

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th 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.

Solution and Metadata

Question: 117
Page: 168
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Simplifying Algebraic Expressions >
Category 2: Arithmetic > Powers and Roots of Numbers > Roots

Explanation: As a general rule, when you need to simplify an expression with radicals in the denominator, use the principle of difference of squares. In this case, since the denominator is rt[n + 1]- rt[n], multiply the top and bottom of the fraction by rt[n + 1]+ rt[n]. Then simplify:

(1/( rt[n + 1]- rt[n])) * (( rt[n + 1]+ rt[n])/( rt[n + 1]+ rt[n]))

= (( rt[n + 1]+ rt[n])/(( rt[n + 1]- rt[n])( rt[n + 1]+ rt[n])))

= (( rt[n + 1]+ rt[n])/((n + 1) - n))

= (( rt[n + 1]+ rt[n])/1)= rt[n + 1]+ rt[n], choice (E).

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