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## Official Guide Explanation:Problem Solving #D16

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.

Question: D16
Page: 22
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Equations >
Category 2: Algebra > Exponents >
Category 3: Arithmetic > Powers and Roots of Numbers > Roots

Explanation: This requires delving into the algebra. To get rid of square root signs, square both sides:

( rt[3 - 2x])2 = ( rt[2x] + 1)2

3 - 2x = 2x + 2 rt[2x] + 1

2 - 4x = 2 rt[2x] (since we still have a square root, move everything else to the other side)

1 - 2x= rt[2x]

(1 - 2x)2 = ( rt[2x])2 (square both sides again)

1 - 4x + 4x2 = 2x

4x2 = 6x - 1, choice (E).

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