Difference between revisions of "2002 AMC 10A Problems/Problem 11"

Revision as of 22:02, 26 December 2008

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
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 10 Problems and Solutions

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 ==Solution==
-We can store a 0.4 MB plus a 0.8 MB file on a disk, or 2 0.7s, but not a 0.8 and a 0.7 together. Hence, our answer is <math>\frac{12}{2}+3+4=\boxed{13\Rightarrow\text{(B)}}</math>.
+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 <math>\boxed{ \text{(B)}\ 13 }</math>.
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Difference between revisions of "2002 AMC 10A Problems/Problem 11"

Revision as of 22:02, 26 December 2008

Problem

Solution

See Also