AMC8 2011

AMC8 2011 · Q6

AMC8 2011 · Q6. It mainly tests Arithmetic misc, Inclusion–exclusion (basic).

In a town of 351 adults, every adult owns a car, a motorcycle, or both. If 331 adults own cars, and 45 adults own motorcycles, how many of the car owners do not own a motorcycle?

一个城镇有351名成人，每位成人都拥有汽车、摩托车或两者皆有。如果有331名成人拥有汽车，45名成人拥有摩托车，那么有多少汽车拥有者不拥有摩托车？

(A) 20 20

(B) 25 25

(D) 306 306

(E) 351 351

Answer

Correct choice: (D)

正确答案：（D）

Solution

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 $331-25=\boxed{\textbf{(D)}\ 306}$ of them don't.

用容斥原理，拥有汽车和摩托车的成人数量为$331+45-351=25$。在$331$名汽车拥有者中，$25$人拥有摩托车，$331-25=\boxed{\textbf{(D)}\ 306}$人不拥有。

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