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## Official Guide Explanation:Data Sufficiency #65

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: 65
Page: 278
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Real Numbers >
Category 2: Arithmetic > Properties of Integers > Other

Explanation: When you subtract one integer from another, the result is one greater than the number of integers between them. (For instance, the difference between 4 and 2 is 2, but there's only one integer between them.) In this case, we're looking for the number of integers between r and s, which means we need the difference, from which we can subtract 1.

Statement (1) gives us the difference, so it's sufficient. Statement (2) gives us the number of integers between r + 1 and s + 1, which is the same as the number of integers between r and s. After all, the difference between r + 1 and s + 1 is the same as the difference between r and s, and the number of integers between them is always 1 less than the difference. Choice (D) is correct.

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