Problem 16 · 2013 Math Kangaroo
Medium
Logic & Word Problems
sum-constraint
30 children took part in a sports competition, playing football and handball. 15 took part in football and 20 took part in handball. How many children took part in both sports?
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Answer: E — 5
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Hint 1 of 3
If you add the football players and the handball players, the children who played both get counted twice.
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Hint 2 of 3
Add 15 and 20 and compare that total to the real number of children, 30.
Still stuck? Show hint 3 →
Hint 3 of 3
The extra amount above 30 is exactly the children who were counted twice.
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Approach: the double-counted children are the ones who played both
- Add the football players and handball players: 15 + 20 = 35.
- But there are only 30 children, so 35 is 5 too many.
- Those extra 5 are the children counted in both lists, so 5 played both, which is answer E.
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