Difference between revisions of "2002 AMC 12A Problems/Problem 9"
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~quantumpsiinverted | ~quantumpsiinverted | ||
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+ | ==Video Solution by Daily Dose of Math== | ||
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+ | https://youtu.be/SZhbxa4X29E | ||
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+ | ~Thesmartgreekmathdude | ||
==See Also== | ==See Also== |
Latest revision as of 12:32, 10 August 2024
- The following problem is from both the 2002 AMC 12A #9 and 2002 AMC 10A #11, so both problems redirect to this page.
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?
Solution
A MB file can either be on its own disk, or share it with a
MB. Clearly it is better to pick the second possibility. Thus we will have
disks, each with one
MB file and one
MB file.
We are left with files of
MB each, and
files of
MB each. Their total size is
MB. The total capacity of
disks is
MB, hence we need at least
more disks. And we can easily verify that
disks are indeed enough: six of them will carry two
MB files each, and four will carry three
MB files each.
Thus our answer is .
Solution 2
Similarly to Solution 1, we see that there must be disks to account for the
MB file. Secondly, since there are
files(for both 0.4 MB and 0.7 MB) left, it is easy to see that the optimal way to place the files would be
files per disks for the 0.4 MB files and hence would require 4 disks.
We are left with files(
MB), where the optimal number of files per disks is
, so the optimal number of disks for this type of file would be
disks. Therefore, the answer is
.
~quantumpsiinverted
Video Solution by Daily Dose of Math
~Thesmartgreekmathdude
See Also
2002 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 8 |
Followed by Problem 10 |
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 12 Problems and Solutions |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.