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# Machines X and Y work at their respective constant rates. Ho

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Manager
Joined: 21 Feb 2009
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Machines X and Y work at their respective constant rates. Ho [#permalink]

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27 Jul 2009, 14:16
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Question Stats:

71% (01:44) correct 29% (01:06) wrong based on 78 sessions

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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 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.

[color=#ff0000]OPEN DISCUSSION OF THIS QUESTION IS HERE: machines-x-and-y-work-at-their-respective-constant-rates-128011.html
[Reveal] Spoiler: OA

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Last edited by Bunuel on 26 Jul 2014, 02:39, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Senior Manager
Joined: 17 Jul 2009
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Concentration: Nonprofit, Strategy
GPA: 3.42
WE: Engineering (Computer Hardware)
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Kudos [?]: 41 [0], given: 9

Re: Machines X and Y work at their respective constant rates. Ho [#permalink]

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27 Jul 2009, 16:44
D.

assuming X takes x amount of time to finish a size of order, and Y takes y amount of time to finish the same size, we need the relationship of x and y

so in statement 1, we have 1/(1/x + 1/y) = 2x/3 =simplify=> xy/(x+y) = 2x/3 => 3y = 2x+2y => y = 2x

and in statement 2, we have y = 2x.

so D. each is sufficient

-edit
after reading whatdahell's reasoning, I neglected the word "hours" in the original question, if the question is looking for an actual number, then we cant calculate the number by any means...the only result we can get is how much faster is x than y, so E probably is a better choice if that's the case

Last edited by sprtng on 27 Jul 2009, 16:55, edited 1 time in total.
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Re: Machines X and Y work at their respective constant rates. Ho [#permalink]

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27 Jul 2009, 16:47
IMO : E - both not suffis

I see that you've chosen C, that means you know why I alone and II alone is not sufficient.

From I, you get the equation: (2/3)x = (xy)/(x+y) ----- (assuming X takes x hours and Y takes y hours to complete the job)

From II, you get x = 2y,

We need to get-> y-x,

from 1 and 2, replacing x= 2y in (i),

(2/3)(2y) = (2yy)/(3y)
-> (4y/3) = (2y/3)
y cancels out so no way of knowing the variable's value. There (E)
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Re: Machines X and Y work at their respective constant rates. Ho [#permalink]

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17 Aug 2009, 08:51
I agree with whatthehell

From the original statement and statement 1 I got the following equation:

1/X + 1/Y = 1/ (2/3*X)

Which is still not sufficent.

Statement 2 alone is not sufficient either...

and when you substitute 2*X for Y :

1/X + 1/2*X = 3/(2*X)
or
3/(2*X) = 3/(2*X)

So the answer is E. Both statements together are not sufficient.
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Re: Machines X and Y work at their respective constant rates. Ho [#permalink]

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17 Aug 2009, 22:12
it is E, by both we arrive at Y =2X, X can take any values.. not sufficient.
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Re: Machines X and Y work at their respective constant rates. Ho [#permalink]

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26 Jul 2014, 02:23
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Machines X and Y work at their respective constant rates. Ho   [#permalink] 26 Jul 2014, 02:23
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# Machines X and Y work at their respective constant rates. Ho

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