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## Official Guide Explanation:Data Sufficiency #66

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: 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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