2009 AMC 12A 第 4 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
4.
从一个存钱罐中取出四枚硬币，存钱罐里有若干一分、五分、十分和二十五分硬币。以下哪一个不可能是这四枚硬币的总价值（单位：分）？
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?
小提示：
如果选出的硬币中至少有一枚一分硬币，总额就不可能是 的倍数。
A selection that includes at least one penny cannot total a multiple of
大提示：
如果没有一分硬币，那么这四枚硬币每枚都至少值 分。
Without a penny, all four coins are worth at least cents each
解答：
如果四枚硬币中有一分硬币，总额不是 的倍数，所以不可能等于列出的五个 的倍数。如果没有一分硬币，每枚硬币至少值 分，所以总额至少是 分。无论哪种情况， 都不可能。
其他数额都能达到：，，，且 。
因此，正确答案是 A。
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.
其他年份的第 4 题
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- 1951 AMC 12
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