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## Official Guide Explanation:Data Sufficiency #81

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: 81
Page: 279
Difficulty: 4 (Moderately Easy)
Category 1: Arithmetic > Descriptive Statistics > other

Explanation: Statement (1) tells us nothing: Between the list of numbers and k < n, there's no way to find the value of n.

Statement (2) is also insufficient. Given a list of 5 (or any odd number of) numbers, the median must be one of the numbers in the set. Since the median of this list is 10 and 10 isn't one of the numbers listed, either k = 10 or n = 10. If we put the numbers in order, it looks like this:

6,(k/n),(k/n),12,17

Either k or n is the median--whichever is larger.

Taken together, the statements are sufficient. Since (1) tells us that n is larger than k, the order of the numbers is:

6,k,n,12,17

The middle number is the median, so n = 10. Choice (C) is correct.

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