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## Official Guide Explanation:Problem Solving #57

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: 57
Page: 160
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Descriptive Statistics > Average
Category 2: Algebra > Linear Equations-One Unk >

Explanation: There are two ways to find the mean of 10, 30, and 50. The traditional way is to add them up and divide by three: ((10 + 30 + 50)/3) = (90/3) = 30. It works, it's reasonably fast, and it's easy. There's another way to instantly see that the average is 30. Any time a set of numbers is equally spaced (consecutive integers, consecutive evens, or numbers all spaced by 20s, like these), the average is equal to the median. The median is simply the middle number, so it's easy enough to spot.

The second step doesn't have a shortcut, unfortunately. If 30 is 5 more than the average of three other numbers, including 20 and 40, the equation can be given as follows:     ((20 + 40 + x)/3) = 25

60 + x = 75

x = 15, choice (A).

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