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## Official Guide Explanation:Data Sufficiency #49

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.

Question: 49
Page: 156
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Properties of Integers > Other

Explanation: Statement (1) is not sufficient. If r and s are integers, the number of possible values of n is 4, as in the example s = 6 and r = 1, where the possible values of n are 2, 3, 4, and 5. However, if r and s are not integers, the number of possible values of n is 5. For example, if r = 5.5 and s = 0.5, n could be 1, 2, 3, 4, and 5.

Statement (2) is not sufficient: without the range between r and s, you cannot find the answer.

Taken together, the statements are sufficient. If r and s are integers and the difference between them is 5, the number of possible values must be 4: s - 1, s - 2, s - 3, and s - 4. Choice (C) is correct.

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