Official Guide Explanation:
Data Sufficiency #66




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Solution and Metadata

Question: 66
Page: 278
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Properties of Integers > Factors and Multiples
Category 2: Arithmetic > Powers and Roots of Numbers > Powers

Explanation: Another way of thinking of the question is: Is t evenly divisible by n?

Statement (1) is insufficient. The only value of n that makes the equation true is 3:

3 = 33 - 2 = 31

We don't know what t is, though, so we can't answer the question.

Statement (2) is also insufficient. If n = 1, then t = 3, so n is a factor of t. However, if n = 2, then t = 9, in which case n is not a factor of t.

Taken together, the statements are sufficient. We know from (1) that n = 3, so t = 33 = 27. 3 is a factor of 27, so the answer is "yes." Choice (C) is correct.

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