Official Guide Explanation:
Data Sufficiency #102




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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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