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Official Guide Explanation:Data Sufficiency #D43

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: D43
Page: 25
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Descriptive Statistics > Average
Category 2: Arithmetic > Descriptive Statistics > other

Explanation: To compare the mean and the median in a set, we need to know how the numbers are distributed. For instance, in a set like {1,1,1,1,10}, the median is lower than the mean, because while the mean is somewhere between 1 and 10, the median is 1. Ultimately, it depends on how many numbers in the set are above and below the mean.

Statement (1) is insufficient. This gives us enough information to calculate the mean (though we don't need to calculate it), but nothing about the median.

Statement (2) is sufficient. The median is less than 50 percent of the terms and greater than 50 percent of the terms, so if 60 percent of the terms are less than the average, the median must be less than the average. Choice (B) is correct.

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