Official Guide Explanation:
Problem Solving #129

Background

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Solution and Metadata

Question: 129
Page: 170
Difficulty: 6 (Moderately Difficult)
Category 1: Word Problems > Rate Problems > other
Category 2: Arithmetic > Fractions >

Explanation: First, establish the range for the number of miles and the number of gallons. If 290 is the number of miles rounded to the nearest ten, the actual number of miles could be as few as 285 and as many as 294. Since the number of gallons is 12, rounded to the nearest gallon, the actual amount could be as little as 11.5 and as much as 12.4. The lowest miles per gallon, then, is the one with the few miles and the most gallons (the largest numerator and the smallest denominator). In this case, that's (285/(12.4)). To find the greatest miles per gallon, look for the opposite: the most miles and the fewest gallons, or (294/(11.5)). Thus, the actual miles per gallon must be between those two numbers. Choice (D) uses endpoints a little bit outside of the ones we chose, but since we know that the miles per gallon must be between our endpoints, it must be inside the slightly wider range of choice (D) as well.

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