Problem 14 · 2021 Math Kangaroo
Medium
Logic & Word Problems
invariantcareful-counting
The Koala ate some leaves from 3 branches. Each branch had 20 leaves. The Koala ate a few leaves from the first branch and then ate as many leaves from the second branch as were left on the first branch. Then it ate 2 leaves from the third branch. How many leaves in total were left on the 3 branches?
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Answer: E — 38
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Hint 1 of 2
Look only at branches 1 and 2 together first — the koala eats from branch 2 exactly what is left on branch 1.
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Hint 2 of 2
The leaves it eats from branch 2 are the same as the leaves still on branch 1, so the two branches together always keep the same amount no matter how much it ate first.
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Approach: branches 1 and 2 together always keep 20, then add branch 3
- Branches 1 and 2 start with 20 + 20 = 40 leaves between them.
- From these two branches the koala eats (some off branch 1) and then the same number off branch 2, so it eats the same amount as the leaves left on branch 1 — meaning branches 1 and 2 together always keep 20 leaves, whatever it nibbled first.
- Branch 3 only loses 2 leaves, so it keeps 20 - 2 = 18.
- Total left = 20 + 18 = 38, so the answer is 38 (E).
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