Question

从一个储钱罐中取出四枚硬币。储钱罐里有一分币、五分币、一角币和二十五分币。以下哪一个数值不可能是这四枚硬币的总价值，单位为美分？

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：钱币整除性极限情形界定

难度评级：940

解答：

要得到 $5$ 的倍数美分，一分币的数量必须是 $5$ 的倍数。只有四枚硬币时，这意味着不能有一分币；但此时每枚硬币至少值 $5$ 美分，总值至少为 $20$ 美分。

所以 $15$ 美分无法得到。其他金额都可以组成： $25 = 10 + 3(5)$ ， $35 = 3(10) + 5$ ， $45 = 25 + 10 + 2(5)$ ，以及 $55 = 25 + 3(10)$ 。

所以正确答案是 A。

To get a multiple of $5$ cents, the number of pennies must be a multiple of $5.$ With only four coins, that means using no pennies, but then the four coins are each worth at least $5$ cents, for a total of at least $20$ cents.

So $15$ cents cannot be made. The others can: $25 = 10 + 3(5),$ $35 = 3(10) + 5,$ $45 = 25 + 10 + 2(5),$ and $55 = 25 + 3(10).$

Thus, the correct answer is A.

2009 AMC 10A 第 2 题

答案：A

难度评级：940

解答：

其他年份的第 2 题