2005 AMC 8 Problem 5
Attempt Problem 5 of the 2005 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 2005 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
5.
Soda is sold in packs of and cans. What is the minimum number of packs needed to buy exactly cans of soda?
Answer: B
Small hint:
Use as many -packs as possible without going over .
Big hint:
After three -packs, finish the remaining cans with the fewest packs.
Solution:
Four packs cannot be enough. Four -packs would contain cans, and replacing any -pack by a smaller pack decreases the total by either or cans. There is no way to decrease by exactly cans to reach .
Five packs do work: three -packs, one -pack, and one -pack contain cans. Therefore, the minimum number is .
Thus, B is the correct answer.
Problem 5 in other years
- 1985 AMC 8
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- 1987 AMC 8
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