Problem 17 · 2022 Math Kangaroo
Hard
Algebra & Patterns
arithmetic-sequence
Some identical glasses are stacked on top of each other. A stack of eight glasses is 42 cm high, and a stack of two glasses is 18 cm high. How high is a stack of six glasses?
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Answer: D — 34 cm
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Hint 1 of 2
Each glass you add on top sticks up by the same fixed amount.
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Hint 2 of 2
Compare the two-glass and eight-glass stacks to find how much one extra glass adds.
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Approach: find how much one extra glass adds, then build up
- Going from 2 glasses to 8 glasses adds 6 glasses and raises the height by 42 − 18 = 24 cm.
- So each extra glass adds 24 ÷ 6 = 4 cm.
- Six glasses is four more than two glasses, so the height is 18 + 4 × 4 = 34 cm.
- So the answer is D.
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