How do you answer these types of questions?

For some reason questions like this do not make sence, can someone help me understand how to find these types of answers?





Jamie's class asked thirty kids about their pets. 8 students own a cat, 15 students own a dog, and 5 students own both a cat and a dog. How many of the students surveyed own no cats?

How do you answer these types of questions?
I think you get bogged down by all the words. I also think this is kind of a trick question, unless you didn't give us all the info.





8 students own a cat


15 students own a dog


5 students own both a cat and a dog.





Nobody said that if you fall into the "own a cat" that you can't own a dog too.





So 8 students own cats. The rest don't. That's 30 - 8 = 22.


With this reasoning, 3 students only own a cat, 5 students own both a cat and a dog, and 10 kids only own a dog. The 5 with both are the overlap. (So 30 - 18 = 12 kids have no cats or dogs, in case you were counting.)





Pictorially its:


C C C CD CD CD CD CD D D D D D D D D D D D D D D D





If all of these categories were truly separate, which is what most of the people answering assume, it would be a different story.





So if the three categories have NO overlap (that is, you own a cat, or you own a dog, or you own one of each, or you own neither), then you get the 17 that other people have given you for an answer.





8 have cats, 5 have both a cat and a dog, the rest don't have a cat. 30 - (8 + 5) = 30 - 13 = 17 with no cat.


But I still think my first answer is right.
Reply:30 students


8 students own a cat


-----------------------------


22 students remaining


15 students own a dog


-------------------------------


7 students remaining


5 students own both a cat and a dog


-----------------------------


2 students remaining


They own nor a cat neither a dog.





Those 15 who own only a dog don't own a cat.





Answers: 15 students own a dog (but not a cat) + 2 students own no pet = total 17 students who own no cat.
Reply:Eight students own a cat, and five students own a cat and a dog, for a total of 13 students who own cats. Therefore, 17 students (30-13) own no cats.
Reply:well, all you have to do is add up 15,8,and five and then watever is left is your answer. So it would be 2 kids that don't have a cat.
Reply:the answer is 17 people do not own cats





if she survayed 30 people and you add up the total of people


who do have pets then minus that from 30 you get 2 then you add the amount of people who only own dogs 15 students plus the 2 students who dont have any pets and it equals 17 people.