Question

汽水以 $6, 12$ 和 $24$ 罐装出售。要正好买 $90$ 罐汽水，最少需要多少包？

Soda is sold in packs of $6, 12$ and $24$ cans. What is the minimum number of packs needed to buy exactly $90$ cans of soda?

$4$

$5$

$6$

$8$

$15$

答案：B

知识点：最优化

难度评级：730

解答：

四包不可能够用。四个 $24$ 罐装共有 $96$ 罐，把其中任意一个 $24$ 罐装换成较小的包装，罐数会减少 $12$ 或 $18$ 。因此不可能恰好从 $96$ 减少 $6$ 罐而得到 $90$ 罐。

五包可以做到：三个 $24$ 罐装、一个 $12$ 罐装和一个 $6$ 罐装共有 $3\cdot24+12+6=90$ 罐。因此最少需要 $5$ 包。

所以正确答案是 B。

Four packs cannot be enough. Four $24$ -packs would contain $96$ cans, and replacing any $24$ -pack by a smaller pack decreases the total by either $12$ or $18$ cans. There is no way to decrease $96$ by exactly $6$ cans to reach $90$ .

Five packs do work: three $24$ -packs, one $12$ -pack, and one $6$ -pack contain $3\cdot24+12+6=90$ cans. Therefore, the minimum number is $5$ .

Thus, B is the correct answer.

2005 AMC 8 第 5 题

答案：B

难度评级：730

解答：

其他年份的第 5 题