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Six machines, each working at the same constant rate [#permalink]
26 Apr 2010, 20:53

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Difficulty:

15% (low)

Question Stats:

84% (01:47) correct
16% (01:10) wrong based on 242 sessions

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?

Re: Six machines, each working at the same constant rate [#permalink]
26 Apr 2010, 21:50

1

This post received KUDOS

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

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.

Re: Six machines, each working at the same constant rate [#permalink]
27 Apr 2010, 05:02

3

This post received KUDOS

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?

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. _________________

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.

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. _________________

Re: Six machines, each working at the same constant rate [#permalink]
19 Jun 2010, 18:52

2

This post received KUDOS

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-

Re: GMAT PREP (PS) [#permalink]
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 _________________

Re: GMAT PREP (PS) [#permalink]
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 _________________

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.

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

I am the master of my fate. I am the captain of my soul. Please consider giving +1 Kudos if deserved!

DS - If negative answer only, still sufficient. No need to find exact solution. PS - Always look at the answers first CR - Read the question stem first, hunt for conclusion SC - Meaning first, Grammar second RC - Mentally connect paragraphs as you proceed. Short = 2min, Long = 3-4 min

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