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## Official Guide Explanation:

Data Sufficiency #87

**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.

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**Solution and Metadata**

**Question****: 87**

Page: 159

Difficulty: **6** (Moderately Difficult)

Category 1: Arithmetic > Properties of Integers > Factors and Multiples

**Explanation:** Statement (1) is insufficient. You can rewrite the equation to set it equal to n (since, after all, we're interested in n): n = 2k + 3, but without knowing anything about k, that doesn't help much. Statement (2) is also insufficient, but provides information about k: if 2k - 4 is divisible by 7, then:

2k - 4 = 7(integer)

2k = 7(integer) + 4

k = ((7(\func{integer}) + 4)/2)

Taken together, the statements are sufficient. Plug in the value of k from (2) into the equation from (1):

n = 2k + 3

n = 2(((7(\func{integer}) + 4)/2)) + 3

n = 7(integer) + 4 + 3

n = 7(integer) + 7

n = 7(integer + 1) = 7(integer)

Thus, n can be shown to be a multiple of 7, and choice (C) is correct.

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