Problem 15 · 2021 Math Kangaroo
Medium
Arithmetic & Operations
differenceswork-backward
On a tall building there are 4 fire escape ladders, as shown. The heights of 3 of the ladders are marked at their tops (32, 48 and 36). What is the height of the shortest ladder?
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Answer: D — 20
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Hint 1 of 2
Each ladder stands on a ledge, and a taller ledge means a taller ladder top — the ledges step up by equal amounts.
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Hint 2 of 2
Find the step between two ladders whose tops you know, then step the same amount down to the shortest ladder.
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Approach: find the equal step between ladder tops and step down to the shortest
- The ladders sit on ledges that rise by the same step each time, so their tops rise by that same step too.
- Two of the marked tops are 48 and 36, a step of 48 - 36 = 12.
- Stepping down 12 from the 32 ladder gives the shortest ladder: 32 - 12 = 20.
- So the shortest ladder is 20 (D).
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