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Three machines, \(K, M,\) and \(P,\) working simultaneously and independently at their respective constant rates, can

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by Gmat_mission » Sun Apr 26, 2020 11:32 am

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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.


[spoiler]OA=A[/spoiler]

Source: Official Guide
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Source: — Data Sufficiency |
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Re: Three machines, \(K, M,\) and \(P,\) working simultaneously and independently at their respective constant rates, ca

by deloitte247 » Sat May 02, 2020 8:27 am
$$Working\ simul\tan eously;\ \frac{1}{K}+\frac{1}{M}+\frac{1}{P}=\frac{1}{24}\min utes$$
Target question => How long does it take machine k working alone at its constant rate to complete the task?

Statement 1 =>
Machines M and P working simultaneously and independently at their respective constant rates can complete the task in 36 minutes
$$\ \frac{1}{M}+\frac{1}{P}=\frac{1}{36}$$
$$Given\ that\ \ \frac{1}{K}+\frac{1}{M}+\frac{1}{P}=\frac{1}{24}$$
$$\ \ \frac{1}{K}+\frac{1}{36}=\frac{1}{24}$$
$$\ \ \frac{1}{K}=\frac{1}{24}-\frac{1}{36}=\frac{3-2}{12}=\frac{1}{12}$$
K= 12 minutes. Statement 1 is SUFFICIENT

Statement 2 =>
Machines K and P working simultaneously and independently at their respective constant rates can complete the task in 48 minutes
$$\ \frac{1}{K}+\frac{1}{P}=\frac{1}{48}$$
$$\ \frac{1}{K}=\frac{1}{48}-\frac{1}{P}=\frac{P-48}{48P}$$
$$K=\frac{48P}{P-48}$$
The value of P is unknown and K's minute cannot be estimated. Hence, statement 2 is NOT SUFFICIENT

Since statement 1 alone is Sufficient, answer = A
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