2011 AMC 8 Problems/Problem 6
Problem
In a town of adults, every adult owns a car, motorcycle, or both. If adults own cars and adults own motorcycles, how many of the car owners do not own a motorcycle?
Solution 1
By PIE, the number of adults who own both cars and motorcycles is Out of the car owners, of them own motorcycles and of them don't.
Solution 2
There are total adults, and own a motorcycle. The number of adults that don't own a motorcycle is . Since everyone owns a car or motorcycle and one who doesn't own a motorcycle owns a car, the answer is .
Solution 3 (answer choices)
Clearly, we can eliminate answer choice , for at least one adult owns motorcycles. It is also fairly obvious that the answer must be in the 300 range, giving us
See Also
2011 AMC 8 (Problems • Answer Key • Resources) | ||
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.