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## Official Guide Explanation:

Problem Solving #148

**Background**

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd 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.

Click here for an example of the PDF booklets. Click here to purchase a PDF copy.

**Solution and Metadata**

**Question****: 148**

Page: 81

Difficulty: **5** (Moderate)

Category 1: Word Problems > Data Interpretation >

Category 2: Arithmetic > Descriptive Statistics > Average

Category 3: Arithmetic > Descriptive Statistics > other

**Explanation:** The median and mean of a set are equal when the set is symmetrical: that is, for every number that is greater than the median, there is a number less than the median that is equally distant from the median. For instance, in the distribution of X, the median is 40. There are 3 occurences of 30 and 3 occurences of 50; because those values are equidistant from the median in opposite directions, they can be said to "cancel each other out." Since all such values in the distribution of X do that, X's mean is equal to its median.

The same can be true of Z, which is symmetrical. (Note that such symmetry is visual, not just arithmetic.) Y, however, is not symmetrical--there are 5 values of 30 against just 2 values of 50, and 3 values of 60 against only one value of 20. Therefore, since X and Z have equal means and medians, the correct choice is (E).

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