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It takes printer A 4 minutes more than printer B to print 40

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It takes printer A 4 minutes more than printer B to print 40 [#permalink] New post 10 Mar 2008, 22:22
It takes printer A 4 minutes more than printer B to print 40 pages. Working
together, the two printers can print 50 pages in 6 minutes. How long in minutes
will it take Printer A to print 80 pages?

12 18 20 24 30
Director
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Re: gmatprep work [#permalink] New post 11 Mar 2008, 06:41
Printer B takes X min to print 40 pages. Per min. it can print 40/X pages.
So Printer A will take X+4 mins. to print 40 pages. Per min. it can print 40/(X+4) pages.

Given that together they can print 50 pages in 6 mins.
So 6(40/X + 40/X+4) = 50

=> 240X + 960 + 240X = 50X^2 + 200X
=> 50X^2 + 280X - 960 = 0
=> 5X^2 + 28X - 960 = 0
=> X = -2.4 which cannot be taken as X cannot be -ve and X = 8

Printer A takes 8+4 = 12 mins. to print 40 pages,
For 80 mins it will take = 2*12 = 24 mins.

Answer D.
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Re: gmatprep work [#permalink] New post 14 Mar 2008, 08:24
abhijit_sen wrote:
Printer B takes X min to print 40 pages. Per min. it can print 40/X pages.
So Printer A will take X+4 mins. to print 40 pages. Per min. it can print 40/(X+4) pages.

Given that together they can print 50 pages in 6 mins.
So 6(40/X + 40/X+4) = 50

=> 240X + 960 + 240X = 50X^2 + 200X
=> 50X^2 + 280X - 960 = 0
=> 5X^2 + 28X - 960 = 0
=> X = -2.4 which cannot be taken as X cannot be -ve and X = 8

Printer A takes 8+4 = 12 mins. to print 40 pages,
For 80 mins it will take = 2*12 = 24 mins.

Answer D.


your answer is right and I followed your method. anyway it took me more than 2 minutes. is there any shortcut? i.e. if a spends 4 minutes more than b to make 40 copies, it would spend 1 more minute to make 10 more copies so 10/x + 10/(x-1) = 50/6
let's divide both members by 10 and get 1/x + 1/(x-1) = 5/6 which makes things much easier. any other solutions?
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Re: gmatprep work [#permalink] New post 14 Mar 2008, 09:50
You can use formula of quarditic equation to solve for 5X^2 + 28X - 960 = 0.

As per it X = (-28 + Sqrt((28)^2 + 4*5*960))/2*5, and (-28 - Sqrt((28)^2 + 4*5*960))/2*5
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Re: gmatprep work [#permalink] New post 14 Mar 2008, 11:26
abhijit_sen wrote:
You can use formula of quarditic equation to solve for 5X^2 + 28X - 960 = 0.

As per it X = (-28 + Sqrt((28)^2 + 4*5*960))/2*5, and (-28 - Sqrt((28)^2 + 4*5*960))/2*5


of course I can but I would avoid calculus in 2 minutes
Re: gmatprep work   [#permalink] 14 Mar 2008, 11:26
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