Problem 21 · 2019 Math Kangaroo
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Logic & Word Problems
sum-constraintcomplementary-counting
There live exactly 15 animals on a farm: cows, cats and kangaroos. We know that exactly 10 animals are not cows and exactly 8 animals are not cats. How many kangaroos live on the farm?
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Answer: B — 3
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Hint 1 of 2
'Not cows' counts cats and kangaroos; 'not cats' counts cows and kangaroos.
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Hint 2 of 2
Find the cows and cats first, then subtract from 15 to get the kangaroos.
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Approach: use the complements
- Not cows = 10, so cows = 15 − 10 = 5.
- Not cats = 8, so cats = 15 − 8 = 7.
- Kangaroos = 15 − 5 − 7 = 3 (B).
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