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

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Intern
Joined: 16 Feb 2012
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Three machines, K, M, and P, working simultaneously and [#permalink]

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01 Jun 2012, 21:01
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5% (low)

Question Stats:

85% (01:38) correct 15% (00:44) wrong based on 123 sessions

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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.

St.#2 From question stem it says that 1/k+1/m+1/p=1/24,so we can find the value of m which is 1/m=1/24-(1/k+1/P), and put the value of m and get the value of k. But why is statement 2 unsuff to get the calue of k?

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: OG data DS question [#permalink]

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02 Jun 2012, 02:01
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rajman41 wrote:
St.#2 From question stem it says that 1/k+1/m+1/p=1/24,so we can find the value of m which is 1/m=1/24-(1/k+1/P), and put the value of m and get the value of k. But why is statement 2 unsuff to get the calue of k?

I believe that you have already figured that I is sufficient.

In st#2 - you can find "m". But now where do you put this value to figure out K?

St 1 alone is sufficient
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Re: Three machines, K, M, and P, working simultaneously and [#permalink]

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30 Jun 2013, 23:59
rajman41 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.

Responding to a pm:

We know that the rate of work of all 3 together is 1/24 i.e. they complete 1/24 of the work every minute.

To know how long machine K will take alone, we need to know the rate of work of machine K (i.e. how much work does machine A alone do every minute).

(I) We know how much work machines M and P do together every minute. They do 1/36 of the work. When all three work together, they complete 1/24 of the work. How does the 1/24 - 1/36 = 1/72 of the work? Of course machine K does it. So this gives us the rate of work of mahcine K and hence time taken by machine K alone = 72 mins. Sufficient

(II) Machines K and P together complete 1/48 of the work every minute. The problem is, out of this 1/48, how much does machine K do? We don't know. Not sufficient.

or assume the work to be 72 units. All three machines together complete it in 24 mins so they do 3 units per min.

(I) M and P together complete 72 units in 36 mins so they make 2 units per min. Hence machine K makes 1 unit per min and will take 72 mins to complete 72 units.
(II) Machines K and P complete 72 units in 48 mins so they make 72/48 units per min, But how many does K make out of them? We don't know.

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

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01 Jul 2013, 00:03
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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] 01 Jul 2013, 00:03
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