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# Machines x and y work at their respective constant rates.

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Intern
Joined: 19 Jun 2009
Posts: 28
Machines x and y work at their respective constant rates. [#permalink]

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17 Oct 2009, 13:32
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Machines x and y work at their respective constant rates. how many more hours does it take machine y, working alone, to fill ta production order of a certain size than it dtakes machine x, working alone?

) machines x and y working together, fill a production order of this size in two thirds the time that machine x, working aloe, does.

2) machine y, working alone, fills a production order of this size in twice the time that machine x, working alone, does

please provide a detailed explanation. thanks.
Math Expert
Joined: 02 Sep 2009
Posts: 39687
Re: machines x and y [#permalink]

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17 Oct 2009, 14:22
Machines X and Y work at their respective constant rates. How many more hours does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?

Let $$x$$ and $$y$$ be the times needed for machines X and Y respectively working alone to fill a production order of this size.

Question: $$y-x=?$$

(1) Machines X and Y, working together, fill a production order of this size in 2/3 the time that machine X, working alone, does --> general relationship: $$\frac{1}{x}+\frac{1}{y}=\frac{1}{total \ time}$$ --> Total time needed for machines X and Y working together is $$total \ time=\frac{xy}{x+y}$$ (general formula) --> given $$\frac{xy}{x+y}=x*\frac{2}{3}$$ --> $$2x=y$$. Not sufficient

(2) Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone, does --> $$2x=y$$, the same info. Not sufficient

(1)+(2) Nothing new. Not Sufficient.

Hope it helps.
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Senior Manager
Joined: 23 May 2008
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12 Dec 2009, 08:51
Hi please tell the approach to solve this question
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Intern
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Joined: 14 Oct 2009
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Schools: Cornell AMBA, Kellogg, Oxford, Cambridge
Re: Tough DS [#permalink]

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12 Dec 2009, 12:52
The question stem is asking "y is how much more than x"
i.e. how much is z in "y = x + z"
As explained by Bunuel, the two statements provide y=zx i.e how many times x is y.
Hence, both statements are not sufficient.
Manager
Joined: 26 Nov 2009
Posts: 164

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13 Dec 2009, 05:11
Machine X and Y work at respective constant rates.How many more hours does it take machine Y,working alone ,to fill a production order of certain size than it takes machine X, working alone ?

1.Machine X and Machine Y working together, fill production order of this size in two-thirds the time that Machine X,working alone does.

2.Machine Y,working alone ,fills a production order of this size in twice the time that machine X ,working alone,does
[Reveal] Spoiler:
E
Manager
Joined: 09 May 2009
Posts: 205
Re: Tough DS [#permalink]

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14 Dec 2009, 09:29
gurpreet07 wrote:
Hi please tell the approach to solve this question

IMO E

as the q is asking exactly how many hrs and we are getting ty=2tx hence none of the statements are suff.
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Re: Tough DS   [#permalink] 14 Dec 2009, 09:29
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# Machines x and y work at their respective constant rates.

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