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Work Rate problem

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Work Rate problem

by gdshamain » Tue May 13, 2014 9:26 am
Machines X and Y work at their constant rates. How many more hours does it take Y working alone to fill an order than it takes X, working alone.

A) X and Y working together fill an order of size in 2/3rd time that machine X, working alone does

B) Y, working alone, fills an order in twice the time that X working alone, does
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Source: — Data Sufficiency |
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by GMATinsight » Tue May 13, 2014 10:43 am
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by Matt@VeritasPrep » Tue May 13, 2014 12:58 pm
Let's have X's rate be 1/x per hour and Y's rate be 1/y per hour, so that X takes x hours and Y takes y hours, respectively, to complete the job.

S1 gives us a relationship between the two rates, but nothing about the actual HOURS each machine takes. (For instance, X and Y together could take 2 hours and X could take 3 hours, or X and Y together could take 20 hours and X could take 30 hours.) INSUFFICIENT

S2 doesn't help either: Y could take 10 hours and X 5 hours, or Y could take 12 hours and X 6 hours, etc.

Combining the two statements still doesn't help, as they say the same thing. We can demonstrate this algebraically as follows:

S1 gives us

(1/x + 1/y) = 3/2 * (1/x)
or
(x+y)/xy = 3/2x
or
(x+y) = 3y/2
or
2x = y

But S1 also tells us that y = 2x, so we haven't got enough equations to solve the problem. Thus the two statements together are INSUFFICIENT, and the answer is E.
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by gdshamain » Tue May 13, 2014 1:09 pm
Thank you, it is clear now!
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by unknown13 » Tue May 13, 2014 8:02 pm
Thanks for explanation
I got the same answer but the problem i made is that
y=2x I assume that this will give me answer if i know any 1 variable. but actual exam they are expecting the tangible value (hard number) and not the equation

thanks again
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