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## Official Guide Explanation:Problem Solving #32

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: 32
Page: 156
Difficulty: 4 (Moderately Easy)
Category 1: Arithmetic > Powers and Roots of Numbers > Roots

Explanation: This is a classic example of the GMAT offering a problem that has a "right way" and a "better way." The "right way" involves multiplying 16 by 20 and 8 by 32, then finding the square root of 576. It works, but it's slow and prone to error. Instead, look for numbers that can be quickly and easily factored out of both terms, as follows:

rt[(16)(20) + (8)(32)]

= rt[(16)(20 + (8)(2))]

= 4 rt[(20 + 16)]

= 4 rt[36]

= 4(6) = 24, choice (B).

There are a variety of different ways to work through this problem, but the most efficient of them resemble the steps shown here.

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