Problem 17 · 2019 Math Kangaroo
Hard
Fractions, Decimals & Percents
complementary-counting
Michaela has 24 animals: dogs, cows, cats and kangaroos. One eighth of the animals are dogs. Three quarters of the animals are not cows, and two thirds are not cats. How many kangaroos does Michaela have?
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Answer: D — 7
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Hint 1 of 2
Convert each fraction into an actual number of animals out of 24.
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Hint 2 of 2
'Not cows' and 'not cats' tell you the cow and cat counts indirectly.
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Approach: find each animal count, then subtract
- Dogs: 24/8 = 3.
- Three quarters are not cows, so cows are one quarter: 24/4 = 6.
- Two thirds are not cats, so cats are one third: 24/3 = 8.
- Kangaroos = 24 − 3 − 6 − 8 = 7.
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