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## Official Guide Explanation:Data Sufficiency #53

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: 53
Page: 277
Difficulty: 5 (Moderate)
Category 1: Algebra > Simplifying Algebraic Expressions >
Category 2: Arithmetic > Descriptive Statistics > Average
Category 3: Arithmetic > Properties of Integers > Other

Explanation: First, simplify the expression. Since all of the parenthetical expressions are added together, we can drop the parentheses altogether:

n - x + n - y + n - z + n - k

4n - x - y - z - k

Statement (1) is sufficient. If the average of x, y, z, and k is n, we can set up an equation:

((x + y + z + k)/4) = n

x + y + z + k = 4n

Going back to the original equation, we can rewrite it as follows:

4n - (x + y + z + k)

Or, substituting what we just discovered:

4n - (4n) = 0

Statement (2) is insufficient. It tells us the relationship between four of the variables (they are consecutive), but nothing about how those relate to n. Choice (A) is correct.

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