Problem 15 · 2020 Math Kangaroo
Hard
Ratios, Rates & Proportions
proportion
Whenever the kangaroo goes up seven steps, the rabbit goes down three steps. When the kangaroo is on step number 56, on which step will the rabbit be?
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Answer: B — 76
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Hint 1 of 2
Every time the kangaroo climbs 7, the rabbit drops 3 — they move in step.
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Hint 2 of 2
Count how many groups of 7 the kangaroo climbed, then drop the rabbit 3 for each.
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Approach: count synchronized moves and apply the rabbit's drop
- Reaching step 56 means the kangaroo made 56 ÷ 7 = 8 climbs.
- In those same 8 moves the rabbit dropped 8 × 3 = 24 steps from 100, landing on 100 − 24 = 76.
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