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

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

## Solution 3

Note that since there are some adults that own both, we can eliminate answer choice $E$. It is fairly obvious that the answer must be in the 300 range, giving us $\boxed{\textbf{(D)}\ 306}$

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