2011 AMC 8 Problem 6

Below is the professionally curated solution for Problem 6 of the 2011 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2011 AMC 8 solutions, or check the answer key.

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Concepts:inclusion-exclusion

Difficulty rating: 870

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?

$20$

$25$

$45$

$306$

$351$

Solution:

We know that $45$ people own motorcycles, so $351 - 45 = 306$ people do not own motorcycles.

Thus, D is the correct answer.

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