Difference between revisions of "2011 AMC 8 Problems/Problem 6"

(Solution 2)
(Solution 3)
 
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==Solution 3==
 
==Solution 3==
  
Note that since there are some adults that own both, we can eliminate answer choice <math>E</math>. It is fairly obvious that the answer must be in the 300 range, giving us <math>\boxed{\textbf{(D)}306}</math>
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Note that since there are some adults that own both, we can eliminate answer choice <math>E</math>. It is fairly obvious that the answer must be in the 300 range, giving us <math>\boxed{\textbf{(D)}\ 306}</math>
  
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2011|num-b=5|num-a=7}}
 
{{AMC8 box|year=2011|num-b=5|num-a=7}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 19:42, 24 August 2020

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 $\boxed{\textbf{(D)}\ 306}$

See Also

2011 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

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