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Six machines, each working at the same constant rate

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Six machines, each working at the same constant rate [#permalink] New post 26 Apr 2010, 20:53
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Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the Job in 8 days?

A. 2
B. 3
C. 4
D. 6
E. 8
[Reveal] Spoiler: OA
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Re: Six machines, each working at the same constant rate [#permalink] New post 26 Apr 2010, 21:50
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zz0vlb wrote:
Six machines, each working at the same constant rate, together can complete a certain job in 12 days.
How many additional machines, each working at the same constant rate, will be needed to complete the Job in 8 days?
a.2
b.3
c.4
d.6
e.8
[Reveal] Spoiler:
3

Source: GMAT Prep

let each machine work at rate of x days
1/x+1/x+1/x+1/x+1/x+1/x = 1/12
6/x = 1/12
x = 72
now y is number of machines needed to complete job in 8 days so,
y/72 = 1/8
y = 9
required = y-x = 3 hence b.
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Re: Six machines, each working at the same constant rate [#permalink] New post 27 Apr 2010, 05:02
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zz0vlb wrote:
Six machines, each working at the same constant rate, together can complete a certain job in 12 days.
How many additional machines, each working at the same constant rate, will be needed to complete the Job in 8 days?

a.2
b.3
c.4
d.6
e.8

[Reveal] Spoiler:
3


Source: GMAT Prep



Another solution which is faster is Since each machine works at a constant rate. The time needs to bought down from 12 to 8. So the new time is 2/3 of the original time. Thus to achieve this we need the rate to be 3/2 of original.

So 3/2* 6 = 9

So we need 9-6 = 3 more machines.
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GMAT PREP (PS) [#permalink] New post 27 Apr 2010, 08:49
Please explain the quick and logical approach
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Re: GMAT PREP (PS) [#permalink] New post 27 Apr 2010, 11:13
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Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?

A. 2
B. 3
C. 4
D. 6
E. 8

Let x be the time needed for 1 machine to complete the job, so rate of one machine is \frac{1}{x} (rate is the reciprocal of time) --> rate of 6 machines would be \frac{6}{x}.

As job=time*rate --> 1=12*\frac{6}{x} --> x=72 days needed for 1 machine to complete the job.

To complete the job in 8 days \frac{72}{8}=9 machines are needed.

Difference: 9-6=3.

Answer: B.
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Re: GMAT PREP (PS) [#permalink] New post 27 Apr 2010, 13:39
Another solution which is faster is Since each machine works at a constant rate. The time needs to bought down from 12 to 8. So the new time is 2/3 of the original time. Thus to achieve this we need the rate to be 3/2 of original.

So 3/2* 6 = 9

So we need 9-6 = 3 more machines.
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Re: Six machines, each working at the same constant rate [#permalink] New post 19 Jun 2010, 18:52
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Actually, this was more simple than I thought. When I first saw this, I started to panic thinking it's a rate question. But then I took a step back, and it was the simplest of calculations.

So here's the deal:

12 days -> 6 machines: 8 days -> ?

8 days means you definitely need more machines than the 6 and in such case the equation looks like-

12 * 6 = 8 * x

Therefore, x = 72 / 8 = 9

So 9-6=3 more machines
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Re: GMAT PREP (PS) [#permalink] New post 16 Jun 2011, 12:56
6*12/1= (6+X)8

X=3
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Re: GMAT PREP (PS) [#permalink] New post 18 Jun 2011, 17:56
Lets look at this way :As the rate of one machine is constant i e 1/(12*6)=1/72 .Even after addition of extra machines the rate will remain the same .Hence,if machines are x now ,the rate becomes 1/8x which is equal to 1/72.
X comes out to be 9 .
Machines added=9-6=3
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Re: GMAT PREP (PS) [#permalink] New post 05 Aug 2011, 03:50
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6 machines require 12 days = 72 machine days
how many machines to do the job in 8 days = \frac{72 machine-days}{8 days} = 9 machines

so, 3 more machines.

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Re: GMAT PREP (PS) [#permalink] New post 05 Aug 2011, 08:02
6 machines - 1 unit of work - 12 days

=> 1 machine = 1/72 of work per day

=> rate of each machine = 1/72

equating work done by 6 machines and 6+x machines

1 = (1/72)(6+x)(8)

=> x = 3

Answer is B.
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Re: GMAT PREP (PS) [#permalink] New post 05 Aug 2011, 12:17
6 machines 12 days...
therefore (6*12)/8=9number of machines required to complete the job in 8 days
Therefore additional machines required=9-6=3
Answer is B
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Re: GMAT PREP (PS) [#permalink] New post 30 Sep 2011, 19:44
Hi, can someone tell me if this is really a level 700 question? I felt like this was so much easier than some of the other questions posted but its labelled as level 700.
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Re: GMAT PREP (PS) [#permalink] New post 30 Sep 2011, 22:22
musicbelle wrote:
Hi, can someone tell me if this is really a level 700 question? I felt like this was so much easier than some of the other questions posted but its labelled as level 700.


Yes its definitely not a 700 level question but then rating of a question on a forum is as per the poster. A 700 level question for me can look like a 500 for you and vice-versa. I would rather concentrate on the take aways from each question
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Re: GMAT PREP (PS) [#permalink] New post 06 Jan 2012, 05:28
Nice question. Nice solutions by many. Thanks all.
Easy one. 3 more machines are required.
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Re: GMAT PREP (PS) [#permalink] New post 06 Jan 2012, 19:53
This is effectively an inverse proportionality problem.

6M --> 12 days --> 1 work
X --> 8 days --> 1 work

X x 8 = 6 x 12
X = 9

Therefore, additional machines = 9-6 = 3
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Re: Six machines, each working at the same constant rate [#permalink] New post 03 Mar 2013, 23:09
zz0vlb wrote:
Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the Job in 8 days?

A. 2
B. 3
C. 4
D. 6
E. 8


6 * rate * 12 = # of Machine * rate * 8.

# of machine =( 6 *12) / 8 = 9.

9 - 6 = 3 additional machines required
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Re: Six machines, each working at the same constant rate   [#permalink] 03 Mar 2013, 23:09
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