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

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04 Sep 2011, 09:45

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79% (00:39) correct
21% (00:58) wrong based on 285 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.

Re: Three machines working in parallel [#permalink]

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04 Sep 2011, 10:18

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

Re: Three machines working in parallel [#permalink]

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07 Dec 2011, 23:16

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

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

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08 Dec 2011, 07:25

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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.

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

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22 May 2014, 04:53

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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?

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.