AMC12 2002 A

AMC12 2002 A · Q9

AMC12 2002 A · Q9. It mainly tests Decimals, Money / coins.

Jamal wants to save 30 files onto disks, each with 1.44 MB space. 3 of the files take up 0.8 MB, 12 of the files take up 0.7 MB, and the rest take up 0.4 MB. It is not possible to split a file onto 2 different disks. What is the smallest number of disks needed to store all 30 files?

Jamal 想把 30 个文件存到软盘中，每张软盘容量为 1.44 MB。3 个文件各占 0.8 MB，12 个文件各占 0.7 MB，其余文件各占 0.4 MB。文件不能拆分存到两张不同的软盘上。存下全部 30 个文件所需的最少软盘数是多少？

(A) 12 12

(B) 13 13

(D) 15 15

(E) 16 16

Answer

Correct choice: (B)

正确答案：（B）

Solution

A $0.8$ MB file can either be on its own disk, or share it with a $0.4$ MB. Clearly it is better to pick the second possibility. Thus we will have $3$ disks, each with one $0.8$ MB file and one $0.4$ MB file. We are left with $12$ files of $0.7$ MB each, and $12$ files of $0.4$ MB each. Their total size is $12\cdot (0.7 + 0.4) = 13.2$ MB. The total capacity of $9$ disks is $9\cdot 1.44 = 12.96$ MB, hence we need at least $10$ more disks. And we can easily verify that $10$ disks are indeed enough: six of them will carry two $0.7$ MB files each, and four will carry three $0.4$ MB files each. Thus our answer is $3+10 = \boxed{\textbf{(B) }13 }$.

一个 $0.8$ MB 的文件要么单独占一张软盘，要么与一个 $0.4$ MB 的文件共用一张软盘。显然第二种更好。因此先用 $3$ 张软盘，每张放一个 $0.8$ MB 文件和一个 $0.4$ MB 文件。剩下 $12$ 个 $0.7$ MB 文件和 $12$ 个 $0.4$ MB 文件。它们总大小为 $12\cdot (0.7 + 0.4) = 13.2$ MB。9 张软盘的总容量为 $9\cdot 1.44 = 12.96$ MB，因此至少还需要 $10$ 张软盘。并且可以验证 $10$ 张确实足够：其中 6 张每张放两个 $0.7$ MB 文件，另外 4 张每张放三个 $0.4$ MB 文件。因此答案为 $3+10 = \boxed{\textbf{(B) }13 }$。

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