Problem:
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 Choices:
A.
B.
C.
D.
E.
Solution:
The number of cat owners plus the number of dog owners is . Because there are only students in the class, there are students who have both.
Because each student has at least a cat or a dog, there are students with a cat but no dog, and students with a dog but no cat. So there are students with both a cat and a dog.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions