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## Official Guide Explanation:Problem Solving #172

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: 172
Page: 176
Difficulty: 5 (Moderate)
Category 1: Algebra > Linear Equations-One Unk >
Category 2: Arithmetic > Powers and Roots of Numbers > Powers

Explanation: If (x - 1)2 = 400, we can get closer to knowing the possible values of x by taking the square root of both sides: (x - 1) = 20 or (x - 1)= - 20. Since the question uses the words "could be," we're warned that there are multiple possible answers; in this case those come from the fact that x - 1 could be positive or negative 20. Solve each one, looking for x - 5 (what the question is asking for):

x - 1 = 20

x = 21

x - 5 = 21 - 5 = 16 (not an answer choice, so we have to keep looking)

x - 1= - 20

x= - 19

x - 5= - 19 - 5= - 24, choice (C).

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