2009 AMC 12A Problem 4
Attempt Problem 4 of the 2009 AMC 12A 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 2009 AMC 12A solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
4.
Four coins are picked out of a piggy bank that contains a collection of pennies, nickels, dimes, and quarters. Which of the following could not be the total value of the four coins, in cents?
Small hint:
A selection that includes at least one penny cannot total a multiple of
Big hint:
Without a penny, all four coins are worth at least cents each
Solution:
If the four coins include a penny, the total is not a multiple of so it cannot equal any of the five listed multiples of If there is no penny, every coin is worth at least cents, so the total is at least cents. Either way, is impossible.
The other amounts are attainable: and
Thus, the correct answer is A.
Problem 4 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
- 1957 AMC 12
- 1958 AMC 12
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