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Three machines, K, M, and P, working simultaneously and independently

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Three machines, K, M, and P, working simultaneously and independently [#permalink]

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New post 22 May 2017, 08:04
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Three machines, K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. How long does it take Machine K, working alone at its constant rate, to complete the task? 

(1) Machines M and P, working simultaneously and 
independently at their respective constant rates, 
can complete the task in 36 minutes. 

(2) Machines K and P, working simultaneously and 
independently at their respective constant rates, 
can complete the task in 48 minutes.

Given:
K, M and P are the machines that working simultaneously and at a constant rate.

Rk + Rm + Rp = performing certain task in 24 minutes. = > Rk + Rm + Rp = 1/24

Rk-$

(1) Rm + Rp = 1/36. => so if we combine the equation of K, M, and P rates, we can find value of Rk =>
Rk + 1/36 = 1/24
Rk = 1/24 – 1/36 = > we can solve for Rk – the statement is sufficient

(2) Here we have Rk + Rp = 1/48. = > from this equation we can only solve for Rm – as individual rate, but there is no way to understand what is Rk or Rp => insufficient.

Correct answer is A.
[Reveal] Spoiler: OA
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Re: Three machines, K, M, and P, working simultaneously and independently [#permalink]

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New post 22 May 2017, 09:41
Hi LalaDi ,

You should at first post the question separately. Then you can proceed ahead with a separate post consisting of the solution.

For example , just go through any of the Timer based problem in the GMAT Forum.

Also the following question comes under DS and not PS. So please be careful next time while posting. :)
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Re: Three machines, K, M, and P, working simultaneously and independently [#permalink]

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New post 22 May 2017, 09:49
Looking at the numerical values given in the question, let me first take the LCM of 24, 36 and 48, which is 144.
Lets say total task is of 144 units.
K+M+P together can do 144 units in 24 minutes

So combined work of (K+M+P) = 144/24 = 6 units per minute

Statement 1. combined work of (M+P) = 144/36 = 4 units per minute
Thus work of K = 6-4 = 2 units per minute. Sufficient.

Statement 2. Combined work of (K+P) = 144/48 = 3 units per minute
But out of these 3 units, we can't say how much K does or P does
Insufficient.

Hence answer is A
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Re: Three machines, K, M, and P, working simultaneously and independently [#permalink]

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New post 22 May 2017, 11:47
LalaDi wrote:
Three machines, K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. How long does it take Machine K, working alone at its constant rate, to complete the task? 

(1) Machines M and P, working simultaneously and 
independently at their respective constant rates, 
can complete the task in 36 minutes. 

(2) Machines K and P, working simultaneously and 
independently at their respective constant rates, 
can complete the task in 48 minutes.

Given:
K, M and P are the machines that working simultaneously and at a constant rate.

Rk + Rm + Rp = performing certain task in 24 minutes. = > Rk + Rm + Rp = 1/24

Rk-$

(1) Rm + Rp = 1/36. => so if we combine the equation of K, M, and P rates, we can find value of Rk =>
Rk + 1/36 = 1/24
Rk = 1/24 – 1/36 = > we can solve for Rk – the statement is sufficient

(2) Here we have Rk + Rp = 1/48. = > from this equation we can only solve for Rm – as individual rate, but there is no way to understand what is Rk or Rp => insufficient.

Correct answer is A.


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Re: Three machines, K, M, and P, working simultaneously and independently   [#permalink] 22 May 2017, 11:47
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