Official Guide Explanation:
Data Sufficiency #87

Background

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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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