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## Official Guide Explanation:Problem Solving #180

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: 180
Page: 178
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Descriptive Statistics > Average
Category 2: Algebra > Linear Equations-Two Unk >

Explanation: At first glance, it doesn't look like there will be enough information to solve this problem, but it's worth investigating further. Since the average of x and y is 60, we can say that x + y = 120. Similarly, if the average of y and z is 80, y + z = 160. If we set one of the equations equal to y, we can substitute into the other one, and have a resulting equation that contains only z, x, and a constant.

y = 160 - z

x + (160 - z) = 120

x - z= - 40

z - x = 40, choice (B).

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