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Manager  Joined: 27 Feb 2010
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Six machines, each working at the same constant rate  [#permalink]

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Question Stats: 80% (01:24) correct 20% (01:35) wrong based on 940 sessions

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 59725

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Welcome to GMAT Club. Below is a solution for the question. Hope it helps

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.

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GMAT 1: 690 Q47 V38 ### Show Tags

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10
6 machines in 12 hours can make 6*12=72 units.
x machines in 8 hours can make x*8=72 units x=9

12-9=3 more machines are needed
hope it helps
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Manager  Joined: 12 Jan 2010
Posts: 223
Schools: DukeTuck,Kelogg,Darden
Re: Six machines, each working at the same constant rate  [#permalink]

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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

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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Re: 6 machines each working @ the same constant rate together  [#permalink]

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11
You can solve this problem without any equations. Just to calculate the rate of 1 machine.

The rate of 1 machine is $$\frac{1}{6*12}=\frac{1}{72}$$ part per day.

So, 1 machine in 8 days can do $$\frac{8}{72}=\frac{1}{9}$$.

So, to finish the job in 8 days we need 9 machines. Therefore 3 additional machines are required.

Intern  Joined: 28 Mar 2010
Posts: 24
Re: Six machines, each working at the same constant rate  [#permalink]

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2
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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Six machines, each working at the same constant rate, together c  [#permalink]

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njss750 wrote:
6 machines each working @ the same constant rate together can complete a certain job in 12 days. How many additional machines are reqd (each working at same constant rate) to finish the job in 8 days?
2
3
4
6
8

Pl xplain with wkgs

6 x 12 = (6+x) x 8

9 = 6+x

x=3
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Six machines, each working at the same constant rate  [#permalink]

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Manager  Joined: 01 Feb 2010
Posts: 173
Re: Six machines, each working at the same constant rate  [#permalink]

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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

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]

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$$Rate of machine = \frac{1}{m}$$

Draw the equation for 6 machines take 12 days:
$$\frac{6}{m}=\frac{1}{12}$$
$$m=72 days$$

Let's look for the number of machines to work for 8 days:
$$\frac{N}{72}=\frac{1}{8}$$
$$N=\frac{72}{8}=9 machines$$

Answer: 9 - 6 machines = 3 machines more

B
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Re: Six machines, each working at the same constant rate  [#permalink]

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This is how I did it

6 machines in 1hr do 1/12 job
in 1 hr, 1 machine do 1/(12*6) job
In 8 days 1 machine do 8/(12*6)=1/9

Thus there is a need of 9 machine.

But I forgot to minus and get the difference so still get this question wrong.
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Six machines, each working at the same constant rate  [#permalink]

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Hi All,

We're told that 6 machines, working at the same constant rate, can finish a job in 12 days. We're asked for the number of EXTRA machines will you need to finish the job in 8 days?

This type of question is easiest to solve if you convert the info into "work units" Here, we start with 6 machines working for 12 days. This equals (6)(12) = 72 machine-days of work to finish the job.

If we wanted to finish the job in 8 days, it would still take 72 machine-days of work, so we'd need 72/8 = 9 machines.

We already have 6 machines, so we need 3 MORE machines to get the job done in 8 days.

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Rich
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Re: Six machines, each working at the same constant rate  [#permalink]

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srkaleem wrote:
Six machines, each working at the same constant rate, together can complete a 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

We are given that six machines, each working at the same constant rate, together can complete a certain job in 12 days. Since rate = work/time and if we consider work as 1, the rate of the six machines is 1/12.

We need to determine how many additional machines, each working at the same constant rate, will be needed to complete the same job in 8 days. In other words we need to determine how many additional machines are needed to work at a rate of 1/8. Since each machine works at the same constant rate, we can use a proportion to first determine the number of machines needed to work at the rate of 1/8.

Our proportion is as follows: 6 machines is to a rate of 1/12 as x machines is to a rate of 1/8.

6/(1/12) = x/(1/8)

72 = 8x

x = 9

So we need 9 – 6 = 3 more machines.

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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.
Senior Manager  Joined: 10 Jul 2013
Posts: 282
Re: Six machines, each working at the same constant rate  [#permalink]

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1
srkaleem wrote:
Six machines, each working at the same constant rate, together can complete a 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

Here, 6 × 1/X = 1/12 or, X=72 . 2nd case, n × 1/72 = 1/8 or, n = 9 . additional = 9-6 = 3
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Re: Six machines, each working at the same constant rate  [#permalink]

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2
6 Machines do $$\frac{1}{12}$$ work in 1 day

We require $$\frac{1}{8}$$ work to be done in 1 day

Multiplication factor$$= \frac{\frac{1}{8}}{\frac{1}{12}} = \frac{1}{8} * 12 = \frac{3}{2}$$

Additional machines required $$= 6 * \frac{3}{2} - 6 = 9 - 6 = 3$$

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Re: Six machines, each working at the same constant rate  [#permalink]

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1
srkaleem wrote:
Six machines, each working at the same constant rate, together can complete a 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

Somehow, I found below method to be working for me -
6 Machines in 12 Days do 1 Work i.e. in notation form
6M * 12D = 1W,
so 1M * 1D = [1/(6*12)] W
How many Machines in 8 Days will complete 1 Work? i.e.
xM * 8D = [(x*8)/(6*12)] W = 1W

Solving for x in [(x*8)/(6*12)] = 1, we get x = 9 i.e. 9 Machines in 8 Days will do 1 Work. So 9-6=3 Machines more are required.

Ans - B
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Re: Six machines, each working at the same constant rate  [#permalink]

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since machine and work in inversely related. thus it is inverse proportion

6 x 12 = 8 x N (let n be the number of person required.)

N=9

thus the number of additional person is 9-6 = 3
Intern  Joined: 10 Dec 2014
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Re: Six machines, each working at the same constant rate  [#permalink]

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1
Six Machines:combined rate=6x
Time=12
Let Job be J

6x*12=J

Let M be the number of machines required to complete job in 8 days
Then
Mx*8=J

6x*12=Mx*8

M=9

Is this approach correct??
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Re: Six machines, each working at the same constant rate  [#permalink]

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1

I wish I could send you a gratitude note for your awesome time efficient approach mentioned
here Logic: more the nos of machines -> less no of days

6

Now we need to decide to multiply by 12/8 or 8/12
Since we need more no of machines to do the work in less time from 12 to 8 days , we need an improper fraction
hence
6 * (12/8) = 9 no of machines.

Additional machines = 9 - 6 = 3

Thanks for detailed post here too

Yes, that's correct!
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Veritas Prep GMAT Instructor Re: Six machines, each working at the same constant rate   [#permalink] 09 Sep 2019, 07:17

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