Problem 1 · 2020 Math Kangaroo
Easy
Algebra & Patterns
arithmetic-sequenceoff-by-one
The kangaroo goes up three steps each time the rabbit goes down two steps. When the kangaroo is on step 9, on which step will the rabbit be?
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Answer: B — 4
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Hint 1 of 2
The kangaroo and rabbit move at the same time but in opposite directions.
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Hint 2 of 2
Find how many moves it took the kangaroo to reach step 9, then move the rabbit down that many times.
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Approach: track two movers step by step
- Each move, the kangaroo climbs 3 steps and the rabbit drops 2 steps.
- To land on step 9 the kangaroo makes 3 moves (3, 6, 9).
- In those same 3 moves the rabbit drops 2 each time, starting from the top step 10: 8, 6, 4.
- So the rabbit ends on step 4.
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