2011 AMC 8 Problems/Problem 6

Problem

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?

$\textbf{(A)}\ 20 \qquad \textbf{(B)}\ 25 \qquad \textbf{(C)}\ 45 \qquad \textbf{(D)}\ 306 \qquad \textbf{(E)}\ 351$

Solutions

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

Solution 2

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, one who doesn't own a motorcycle owns a car, so the answer is $\boxed{\textbf{(D)}\ 306}$ .

2011 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 5	Followed by Problem 7
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All AJHSME/AMC 8 Problems and Solutions

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2011 AMC 8 Problems/Problem 6

Contents

Problem

Solutions

Solution 1

Solution 2

See Also