Mathematics > Standard Multiple Choice
Read the following SAT test question and then click on a button to select your answer.
In a community of 416 people, each person owns a dog or a cat or both. If there are 316 dog owners and 280 cat owners, how many of the dog owners own no cat?
(A) 36
(B) 100
(C) 136
(D) 180
(E) 316
The Correct answer is C.
Explanation
To solve this problem, you must realize that some of the 
also own cats and some of the 
cat owners also own dogs. This has to be true because 
is more than 
! The question asks how many of the dog owners do not own cats. To solve the problem, first find the number of people who own both a dog and a cat. To do this, let 
equal the number who own both a dog and a cat. Then 
. (Note: Adding 
and 
counts 
twice, so 
must be subtracted from the sum to get 
.) Next, the equation 
can be solved for 
, yielding 
. Finally, the number of dog owners who own no cat is 
.