Official Guide Explanation:
Data Sufficiency #D32

Background

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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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