2002 AMC 10A Problems/Problem 11

Problem

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?

$\text{(A)}\ 12 \qquad \text{(B)}\ 13 \qquad \text{(C)}\ 14 \qquad \text{(D)}\ 15 \qquad \text{(E)} 16$

Solution

Our best possibilities are storing a 0.8 and a 0.4, two 0.7, or three 0.4s on one disk. On three disks, we put a 0.8 and a 0.4 each. On 6 other disks, we put two 0.7s each. We put the remaining 12 0.4s in 4 disks in groups of 3. As these take care of all the files, and it is easy to verify that we cannot use less space, our answer is $\boxed{ \text{(B)}\ 13 }$ .

2002 AMC 10A (Problems • Answer Key • Resources)
Preceded by Problem 10	Followed by Problem 12
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2002 AMC 10A Problems/Problem 11

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