Question

Jamal 想把 $30$ 个电脑文件存到软盘上，每张软盘容量为 $1.44$ 兆字节（MB）。其中三个文件各需要 $0.8$ MB，另有 $12$ 个各需要 $0.7$ MB，剩下 $15$ 个各需要 $0.4$ MB。一个文件不能拆分到多张软盘上。最少需要多少张软盘？

Jamal wants to store $30$ computer files on floppy disks, each of which has a capacity of $1.44$ megabytes (mb). Three of his files require $0.8$ mb of memory each, $12$ more require $0.7$ mb each, and the remaining $15$ require $0.4$ mb each. No file can be split between floppy disks. What is the minimal number of floppy disks that will hold all the files?

$12$

$13$

$14$

$15$

$16$

答案：B

知识点：最优化极限情形界定

难度评级：1420

解答：

文件总大小为 $3(0.8)+12(0.7)+15(0.4)$ $=16.8$ 兆字节。任何装有 $0.8$ 兆字节文件的软盘，只能再放一个 $0.4$ 兆字节文件，因为 $0.8+0.7\gt 1.44$ 。因此每张这样的软盘至少浪费 $0.24$ 兆字节，三张共至少浪费 $0.72$ 兆字节，有效需求至少为 $16.8+0.72=17.52$ 兆字节，所以至少需要 $\left\lceil\dfrac{17.52}{1.44}\right\rceil=13$ 张软盘。

这个数可以达到： $3$ 张各放一个 $0.8$ 兆字节文件和一个 $0.4$ 兆字节文件； $6$ 张各放两个 $0.7$ 兆字节文件； $4$ 张各放三个 $0.4$ 兆字节文件。

所以正确答案是 B。

The files need $3(0.8)+12(0.7)+15(0.4)$ $=16.8$ mb. On any disk holding a $0.8$ mb file, only one $0.4$ mb file fits alongside it (since $0.8+0.7\gt 1.44$ ), leaving at least $0.24$ mb wasted. Across the three such disks that is at least $0.72$ mb, so the effective demand is at least $16.8+0.72=17.52$ mb, requiring at least $\left\lceil\dfrac{17.52}{1.44}\right\rceil=13$ disks.

This is achievable: $3$ disks each hold one $0.8$ file and one $0.4$ file, $6$ disks each hold two $0.7$ files, and $4$ disks each hold three $0.4$ files.

Thus, the correct answer is B.

2002 AMC 10A 第 11 题

答案：B

难度评级：1420

解答：

其他年份的第 11 题