Problem 10 · 2011 Math Kangaroo
Medium
Logic & Word Problems
careful-countingcasework
All the children in a class have at least one pet, and at most two pets. They write down how many pets they have together. Two children each have a dog and a fish. Three each have a cat and a dog. No child has two cats. Altogether they have eight cats, six dogs, and two fish. How many children are in the class?
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Answer: A — 11
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Hint 1 of 2
Sort the children by which pets they own, using the given groups first.
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Hint 2 of 2
Account for all 8 cats, 6 dogs and 2 fish without giving anyone two cats.
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Approach: tally each pet type
- 2 children have dog+fish (using both fish and 2 dogs); 3 children have cat+dog (using 3 cats and 3 dogs).
- Dogs left: 6 − 5 = 1, so one child has just a dog. Cats left: 8 − 3 = 5, so five children have just a cat (no one has two cats).
- Children = 2 + 3 + 1 + 5 = 11, answer A.
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