Problem 10 · 2009 Math Kangaroo
Medium
Ratios, Rates & Proportions
proportion
In a park there are some cats and some dogs. The number of cats’ feet is twice the number of dogs’ noses. The number of cats is …… the number of dogs.
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Answer: B — half the size
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Hint 1 of 2
Count carefully: how many feet does a cat have, and how many noses does a dog have?
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Hint 2 of 2
Each cat brings 4 feet, but each dog brings only 1 nose, so try a small picture and compare.
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Approach: try a small case and spot the pattern
- A cat has 4 feet and a dog has 1 nose, so 1 cat already makes 4 feet.
- We need cats' feet to be twice the dogs' noses: try 1 cat (4 feet) and 2 dogs (2 noses) — 4 is twice 2, it works!
- Here 1 cat goes with 2 dogs, so there are half as many cats as dogs every time.
- So the number of cats is half the size of the number of dogs — answer B.
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