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

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01 Jun 2012, 20:01

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86% (01:39) correct
14% (00:42) wrong based on 119 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?

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?

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.

Answer A

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.

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.

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