1992 AMC 8 Problem 25
Attempt Problem 25 of the 1992 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1992 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
25.
One half of the water is poured out of a full container. Then one third of the remainder is poured out. Continue the process: one fourth of the remainder for the third pouring, one fifth of the remainder for the fourth pouring, and so on. After how many pourings does exactly one tenth of the original water remain?
Answer: D
Small hint:
After the first pouring remains; after the second remains
Big hint:
The remaining fraction telescopes: after pourings it is ; set this equal to
Solution:
After the th pouring, the fraction remaining is which telescopes to
Setting gives
Thus, the correct answer is D .
Problem 25 in other years
- 1985 AMC 8
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- 1987 AMC 8
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