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

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

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17 Jan 2010, 13:01
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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. 3
B. 4
C. 6
D. 9
E. 12
[Reveal] Spoiler: OA
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17 Jan 2010, 16:26
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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

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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05 Jun 2010, 13:08
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"
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21 Jun 2010, 08:21
@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):

Assumption:
$$\frac{1}{A}+\frac{1}{B}=\frac{1}{x}$$

$$\frac{1}{A}=\frac{1}{36}$$
$$\frac{1}{B}=\frac{1}{18}=\frac{2}{36}$$
$$x=2$$ = combined consumed time for task

$$y(\frac{3}{36})=\frac{1}{2}$$

And in order to end up with 18/36 = 1/2 we need y to be 6 - so one can assume that we need 6machines of type R

Thanks

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21 Jun 2010, 15:27
Beraterschwein, I think your solution is good. There is nothing wrong with it.
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22 Jun 2010, 07:12
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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22 Jun 2010, 07:22
I too get the feeling there has been a typo.. the calculations done other wise seem perfect.
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26 Jul 2010, 05:50
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.

QA = 6
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Re: A company has two types of machines,type R and type S. [#permalink]

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26 Jan 2014, 14:02
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Re: A company has two types of machines,type R and type S. [#permalink]

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13 Jan 2016, 19:04
Bunuel, can you fix the typo in the original question and move this question to 500-Level?
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Re: A company has two types of machines,type R and type S. [#permalink]

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17 Feb 2016, 10:11
Is it really a 700 question? I think the only thing that makes the question difficult is the typo
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Re: A company has two types of machines,type R and type S.   [#permalink] 17 Feb 2016, 10:11
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