AMC 8 2011 Problem 6
AMC8 2011 年第 6 题
基本计数原理★★☆☆☆
In a town of 351 adults, every adult owns a car, motorcycle, or both. If 331 adults own cars and 45 adults own motorcycles, how many of the car owners do not own a motorcycle?
在一个有 351 个成年人的小镇，每个成年人都有汽车，摩托车或者两者兼具。若 331 人有汽车，45 人有摩托车，那么拥有汽车的人当中，有多少人没有摩托车？
- A.20
- B.25
- C.45
- D.306
- E.351
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
By PIE, the number of adults who own both cars and motorcycles is 331+45-351=25. Out of the 331 car owners, 25 of them own motorcycles and 331-25=306 of them don't.
There are 351 total adults, and 45 own a motorcycle. The number of adults that don't own a motorcycle is 351 - 45 = 306. Since everyone owns a car or motorcycle and one who doesn't own a motorcycle owns a car, the answer is 306. Clearly, we can eliminate answer choice , for at least one adult owns motorcycles. It is also fairly obvious that the answer must be in the 300 range, giving us 306
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