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

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Three machines, K, M, and P, working simultaneously and [#permalink]  04 Sep 2011, 08:45
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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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: three-machines-k-m-and-p-working-simultaneously-and-143489.html
[Reveal] Spoiler: OA
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Re: Three machines working in parallel [#permalink]  04 Sep 2011, 08:57
1
KUDOS
From the data provided in the Q

1/k + 1/m + 1/p = 1/24

(1) says
1/m + 1/ p = 1/36
which along with the eq from the Qs, gives
1/k = 1/24 - 1/36 = 1/72

means k will take 72 mins ,working alone at its constant rate, to complete the task

(2) says
1/k + 1/p = 1/48
from this data , we can ind the working rate of m/c M.

So (1) alone is sufficient
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Re: Three machines working in parallel [#permalink]  04 Sep 2011, 09:18
buddy... in the exam you wouldnt want to actually sit and <solve> such problems. In some DS questions u can conclude without actually solving them... this is one such type of a problem

if u really want a detailed explanation, here it is...

let mc K do the task individually in k mins
similarly P in p mins
and M in m mins

so K's work in 1 min is 1/k
M's work similarly is 1/m
and P's is 1/p

since working together they can complete the work in 24 mins, they complete 1/24th work in 1 min

= > 1/k + 1/m + 1/p = 1/24 ------ (1)

the remainder of the part, is pretty much the same as Depaulian has suggested. hence ans is A
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Re: Three machines working in parallel [#permalink]  05 Oct 2011, 11:23
all three working together it is 24

so 1/K+1/M+1/P = 1/24

1. 1/M+1/P = 1/36

Applying this we can find 1/k

2. WE cannot fin 1/K with this

Ans A
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Re: Three machines working in parallel [#permalink]  07 Dec 2011, 09:19
Depaulian wrote:
From the data provided in the Q

1/k + 1/m + 1/p = 1/24

(1) says
1/m + 1/ p = 1/36
which along with the eq from the Qs, gives
1/k = 1/24 - 1/36 = 1/72

means k will take 72 mins ,working alone at its constant rate, to complete the task

(2) says
1/k + 1/p = 1/48
from this data , we can ind the working rate of m/c M.

So (1) alone is sufficient

Can someone please explain the reasoning behind flipping them like that?

I know that the amount of work produced is Rate * time = work. How is that used in this answer?

Thank you
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Re: Three machines working in parallel [#permalink]  07 Dec 2011, 22:16
viks4gmat wrote:
buddy... in the exam you wouldnt want to actually sit and <solve> such problems. In some DS questions u can conclude without actually solving them... this is one such type of a problem

if u really want a detailed explanation, here it is...

let mc K do the task individually in k mins
similarly P in p mins
and M in m mins

so K's work in 1 min is 1/k
M's work similarly is 1/m
and P's is 1/p

since working together they can complete the work in 24 mins, they complete 1/24th work in 1 min

= > 1/k + 1/m + 1/p = 1/24 ------ (1)

the remainder of the part, is pretty much the same as Depaulian has suggested. hence ans is A

This is a gr8 explanation- thanks i missed the qs
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Re: Three machines, K, M, and P, working simultaneously and [#permalink]  08 Dec 2011, 06:25
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1/k+1/M+1/p=1/24. K=?

Statement 1: we have value for 1/M+1/P. Can solve for K. Sufficient.
Statement 2: we have value for 1/K+1/P. Can solve for M but not for K. Not sufficient.
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Re: Three machines, K, M, and P, working simultaneously and [#permalink]  22 May 2014, 03:53
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Re: Three machines, K, M, and P, working simultaneously and [#permalink]  22 May 2014, 04:21
Expert's post
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?

Say k, m, and p are the numbers of minutes machines K, M, and P take, respectively, to complete the task. Then we have that $$\frac{1}{k}+\frac{1}{m}+\frac{1}{p}=\frac{1}{24}$$.

(1) Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes --> $$\frac{1}{m}+\frac{1}{p}=\frac{1}{36}$$, thus $$\frac{1}{k}+\frac{1}{36}=\frac{1}{24}$$ --> we can find the value of $$k$$. Sufficient.

(2) Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes --> $$\frac{1}{k}+\frac{1}{p}=\frac{1}{48}$$. The value of k cannot be determined from the data we have. Not sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: three-machines-k-m-and-p-working-simultaneously-and-143489.html

ALL OG13 QUESTIONS WITH SOLUTIONS: the-official-guide-quantitative-question-directory-143450.html
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Re: Three machines, K, M, and P, working simultaneously and   [#permalink] 22 May 2014, 04:21
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