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If 16 machine can finish a job in 36 days, then how many more machines

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If 16 machine can finish a job in 36 days, then how many more machines  [#permalink]

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New post 10 May 2015, 11:04
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If 16 machine can finish a job in 36 days, then how many more machines would be needed to finish the job in one -third less time?

a. 4
b. 8
c. 10
d. 12
e. 16
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Re: If 16 machine can finish a job in 36 days, then how many more machines  [#permalink]

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New post 10 May 2015, 12:13
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You might think of this in a management context - we can use the principle of 'person-hours' to solve any problem where we have identical workers. So, using simpler numbers, suppose you know that 6 identical employees, working simultaneously, would finish a job in 5 hours. Then that job requires 6*5 = 30 total hours of person-work. If instead you wanted the job done in 3 hours, you'd assign 30/3 = 10 employees to do the job, because you want to get a total of 30 hours of work from the employees.

We can solve this problem identically. If 16 machines (identical ones, I assume) work simultaneously for 36 days, they will do a total of 16*36 machine-days of work. So the job requires 16*36 days of machine work in total. We instead want the job done in 1/3 less time, so in 24 days. So we'll need 16*36/24 = 24 machines, or 8 additional machines.
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Re: If 16 machine can finish a job in 36 days, then how many more machines  [#permalink]

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New post 10 May 2015, 19:28
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Hi,

16 machines can finish a JOB in 36 days.
Let me re frame the sentence here:

In 36 days 16 machines can finish a JOB.
In 1 day 16 machines can finish (1/36) part of JOB
In 1 day 1 machine can finish 1/(36*16) part of JOB---------------------------- (1)

We know that the JOB has to be completed in one-third less time which means 36-1/3*(36) = 24 days

From (1)
In 24 days 1 machine can finish 24/(36*16) part of JOB i.e. 1/24 part of JOB
So you need 24 machines to finish the JOB in 24 days.

So number of extra machines that you need is 24 -16 = 8

Answer B

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Re: If 16 machine can finish a job in 36 days, then how many more machines  [#permalink]

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New post 10 May 2015, 21:12
2
Turkish wrote:
If 16 machine can finish a job in 36 days, then how many more machines would be needed to finish the job in one -third less time?

a. 4
b. 8
c. 10
d. 12
e. 16


Use "Work-Rate using Joint Variation" approach discussed here: http://www.veritasprep.com/blog/2013/02 ... variation/

36 days - 16 machines
24 days (1/3rd less time) - ?? machines

Since the number of machines required will increase, you will multiply 16 by 36/24 (greater than 1).
New number of machines = 16 * (36/24) = 24

So you need 8 extra machines
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Re: If 16 machine can finish a job in 36 days, then how many more machines  [#permalink]

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New post 27 Jul 2018, 09:49
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: If 16 machine can finish a job in 36 days, then how many more machines &nbs [#permalink] 27 Jul 2018, 09:49
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