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## Official Guide Explanation:Problem Solving #155

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: 155
Page: 174
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Powers and Roots of Numbers > Roots
Category 2: Algebra > Linear Equations-One Unk >
Category 3: Word Problems > Other >

Explanation: A positive number x is multiplied by 2:    2x

...and this product is then divided by 3:    ((2x)/3)

If the positive square root of the result:     rt[((2x)/3)]

equals x:    x= rt[((2x)/3)]

What is the value of x? Square both sides:

x2 = ((2x)/3), multiply both sides by 3:

3x2 = 2x, divide by x:

3x = 2, divide by 3:

x = (2/3), choice (D).

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