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A company has dozens of identical printers. The manager has 26 Nov 2006, 08:54
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A company has dozens of identical printers. The manager has been informed that, in order to print 300 copies of a flyer in twenty minutes, 7 printers need to be used. What is the minimum number of printers that MIGHT be able to print 800 copies in 15 minutes?

(A) 20 (B) 21 (C) 22 (D) 23 (E) 24



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A company has dozens of identical printers. The manager has 26 Nov 2006, 10:34
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300 copies in 20 minutes means 300 / 20 copies per minutes

this means we are given that to print 15 copies per minute 7 printers are needed

800 copies in 15 min means 800/15 = 53.3 copies / min

therefore,
15 c/m ----- 7
53.3c/m ----- x

cross multiply, x = 7 * 53.3 / 15 ~ 7 * 54/ 15 ~ 24

which is choice E.
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A company has dozens of identical printers. The manager has 27 Nov 2006, 04:45
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MIGHT :?:

I don't understand....
I found also a value >24, so the minimum would have been 25 printers... Closest answer E.
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Fig
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A company has dozens of identical printers. The manager has 27 Nov 2006, 05:25
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As others, I'm out of the range offered by answer choices :)

Let s be the speed of a printer (copies per min)

As we don't know the exact speed of a printer, we can use the number of printers assigned to accomplish one task in order to determine the range of possible printer's speed.

7 printers is enough, thus 6 printers is not enough.

We have so:

7*20*s >= 300 > 6*20*s
=> 15/7 <= s < 15/6

Let n be the number of printer working for the job of 800 copies in 15 min.

To find n, we have to be sure that the worst case, that of the minimum speed, works. We can thus compare the speed expected to the minimum speed obtained

For Smin = 15/7
=> Smin * n >= 800/ 15 = 160/3
<=> n > 160/3 * 7/15 = 7/3 * 160/(5*3) = 7*32/9 approximated to 24,88 < 25

To be sure, we need to have 25 printers working together on the task.
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A company has dozens of identical printers. The manager has 27 Nov 2006, 05:32
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In 20 minutes, 1 printer prints 300/7 prints
In 15 minutes, 1 printer prints 300/7*15/20 prints = 225/7 prints

225/7 prints in 15 minutes by 1 printer
800 prints in 15 minutes by 7/225*800 printers=24+8/9 printers
which makes the choice E to be correct answer.
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A company has dozens of identical printers. The manager has Updated on: 01 Dec 2006, 03:37
Originally posted by Fig on 27 Nov 2006, 08:04.
Last edited by Fig on 01 Dec 2006, 03:37, edited 2 times in total.
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Sumithra
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The key word is might.

Do you mean to say it is min., so 20?
Show more


So it should be that we are looking for minumum without being 100% sure to achieve the task :)

For Smin = 15/6
=> Smin * n >= 800/ 15 = 160/3
<=> n > 160/3 * 6/15 = 320/(5*3) = 64/3 approximated to 21,33.

Thus, it should be 22 and the answer (C) :)
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A company has dozens of identical printers. The manager has 28 Nov 2006, 22:17
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High school style

Copies Time Printer

300 20 7

800 15 x

x = (800/300)*(20/15)*7 = ~24
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halahpeno
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A company has dozens of identical printers. The manager has 30 Nov 2006, 15:01
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I get E as well.

300 copies by 7 printers in 20 minutes = ~2.1 copies/min

multiply the copies by 15 to get # of copies in 15 min by one printer: ~32

divide the 800 copies by the number of copies per printer per 15 min: 25

Since 25 is an estimate, I choose D for being the closest.

Not an exact science, but so be it!



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