Official Guide Explanation:
Data Sufficiency #53




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Solution and Metadata

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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