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A company has two types of machines,type R and type S. [#permalink]

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17 Jan 2010, 12:01

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A company has two types of machines, type R and type S. Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 18 hours. If the company used the same number of each type of machine to do job in 12 hours,how many machine R were used?

A company has two types of machines,type R and type S.Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 18 hours .If the company used the same number of each type of machine to do job in 12 hours,how many machine R were used? A.3 B.4 C.6 D.9 E.12 Answer:C But how?

Rate of A - \(\frac{1}{36}\) job/hour, rate of x machines of A - \(\frac{1}{36}x\) job/hour; Rate of B - \(\frac{1}{18}\) job/hour, rate of x machines of B - \(\frac{1}{18}x\) job/hour, (same number of each type);

Remember that we can sum the rates, hence combined rate of A and B is \(\frac{1}{36}x+\frac{1}{18}x=\frac{3}{36}x=\frac{1}{12}x\) job/hour.

We are told that together equal number (x in our case) of machines A and B can do the job (1 job) in 12 hours --> \(Time*Rate=12*\frac{1}{12}x=1=Job\) --> \(x=1\).

There is no correct answer listed. There must be a typo in the stem or in the answer choices.

As you stated that the correct answer is C (6), I'd suggest that there should be 2 hours instead of 12. If so, then the last step: \(Time*Rate=2*\frac{1}{12}x=1=Job\) --> \(x=6\).
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A company has two type of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hours and machine of type S does the same job in 18 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used.

3 4 6 9 12

this is confusing me " company used the same number of each type of machine to do the job in 2 hours"

@bunuel, not sure whether I am right on this, but could I go for the following solution as well (assuming that we are looking for a combined time of 2 hours):

How can you assume x=2? If same no. of machines S and R taken together, then the task will be done in exactly 12 hours requiring 1 machine of each type. As Bunuel mentioned, this may be a typo error for 12 instead of 2.
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yes there is a typo in the question, I got the same ques on my GMAT PREP last week, and the questions goes as:

A company has two types of machines,type R and type S.Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 18 hours .If the company used the same number of each type of machine to do job in 2 hours,how many machine R were used?

So for a job to be done in 2 hours R = 1/2

R_a(Rate of Machine R) = 1/36 R_s(Rate of Machine S) = 1/18 Lets say x machines are used to attain the desired rate, thus x/36+x/18 = 1/2 (Desired R =1/2 i.e. to complete the job in 2 hours) (x+2x)/36 = 1/2 3x/36 = 1/2 x = 6.

Re: A company has two types of machines,type R and type S. [#permalink]

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26 Jan 2014, 13:02

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Re: A company has two types of machines,type R and type S. [#permalink]

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28 Sep 2016, 20:58

samrand wrote:

A company has two types of machines, type R and type S. Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 18 hours. If the company used the same number of each type of machine to do job in 12 hours,how many machine R were used?

A. 3 B. 4 C. 6 D. 9 E. 12

Can someone correct the typo please.
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Re: A company has two types of machines,type R and type S.
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28 Sep 2016, 20:58