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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

答案和解析

答案：C

解析：

To solve this problem, you must realize that some of the 316 dog owners also own cats and some of the 280 cat owners also own dogs. This has to be true because 316 + 280 is more than 416, 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 b equal the number who own both a dog and a cat. Then 416 = 316 + 280-b. (Note: Adding 316 and 280 counts b twice, so b must be subtracted from the sum to get 416.) Next, the equation 416 = 596-b can be solved for b, yielding b = 180. Finally, the number of dog owners who own no cat is 316-180 = 136.