Question

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?

$15$

$25$

$35$

$45$

$55$

答案：A

知识点：钱币倍数分类讨论

难度评级：1200

解答：

如果四枚硬币中有一分硬币，总额不是 $5$ 的倍数，所以不可能等于列出的五个 $5$ 的倍数。如果没有一分硬币，每枚硬币至少值 $5$ 分，所以总额至少是 $20$ 分。无论哪种情况， $15$ 都不可能。

其他数额都能达到： $25 = 10 + 5 + 5 + 5$ ， $35 = 10 + 10 + 10 + 5$ ， $45 = 25 + 10 + 5 + 5$ ，且 $55 = 25 + 10 + 10 + 10$ 。

因此，正确答案是 A。

If the four coins include a penny, the total is not a multiple of $5,$ so it cannot equal any of the five listed multiples of $5.$ If there is no penny, every coin is worth at least $5$ cents, so the total is at least $20$ cents. Either way, $15$ is impossible.

The other amounts are attainable: $25 = 10 + 5 + 5 + 5,$ $35 = 10 + 10 + 10 + 5,$ $45 = 25 + 10 + 5 + 5,$ and $55 = 25 + 10 + 10 + 10.$

Thus, the correct answer is A.

2009 AMC 12A 第 4 题

答案：A

难度评级：1200

解答：

其他年份的第 4 题