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## Official Guide Explanation:

Data Sufficiency #102

**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.

Click here for an example of the PDF booklets. Click here to purchase a PDF copy.

**Solution and Metadata**

**Question****: 102**

Page: 281

Difficulty: **5** (Moderate)

Category 1: Word Problems > Rate Problems > Speed

Category 2: Word Problems > Rate Problems > Combined Rate

**Explanation:** The main question in this problem is the speed at which car X is pulling away from car Y--that is, the difference between their speeds. If car X is moving 5 miles per hour faster, it will get five miles ahead per hour. Since car X is now 1 mile ahead and we want to know when it will be 2 miles ahead of car X, we have distance (1 miles), but we need rate (the difference between X's and Y's rates) to find time.

Statement (1) is sufficient: given both rates, we can find the different (10 miles per hour), so we can solve for time. Statement (2) is also sufficient. Given a distance ((1/2) mile) and a time (3 minutes), you can solve for rate, and then use that rate to find the time the question is asking for. Choice (D) is correct.

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