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## Official Guide Explanation:

Data Sufficiency #D32

**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.

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**Solution and Metadata**

**Question****: D32**

Page: 24

Difficulty: **6** (Moderately Difficult)

Category 1: Arithmetic > Descriptive Statistics > other

Category 2: Algebra > Inequalities > other

**Explanation:** First, put the integers in order: 3, 4, 5, 6; x and y could each go anywhere in that list, depending on what we learn about them. Right now, the range could be as little as 3; in order for the range to be greater than 9, there are three possibilities: one of the variables is greater than 12, one of the variables is less than -3, or the two variables are more than 9 apart.

Statement (1) is insufficient. It is possible that x = 1 and y = 4, in which case the range is less than 9. However, it is also possible that x = 1 and y = 15, in which case the range is greater than 9.

Statement (2) is also insufficient. x and y could be 4 and 5, in which case the range is less than 9. It is also possible that x and y could be 14 and 15, in which case the range must be greater than 9.

Taken together, the statements are sufficient. The smallest x could be is 4. Since y > 3x, y must be greater than 12. If y is greater than 12, we've already established that the range must be greater than 9. Choice (C) is correct.

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