2008 AMC 8 Problem 11
Attempt Problem 11 of the 2008 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2008 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
11.
Each of the students in the eighth grade at Lincoln Middle School has one dog or one cat or both a dog and a cat. Twenty students have a dog and students have a cat. How many students have both a dog and a cat?
Answer: A
Small hint:
Adding dog owners and cat owners counts students with both pets twice.
Big hint:
Use inclusion-exclusion with the total number of students as the union.
Solution:
The number of people that have both animals is equal to the number of people that own a cat plus the number of people that own a dog minus the number of people that own either.
Therefore, the number of people who own both is
Thus, the answer is A .
Problem 11 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
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