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Machine R and machine S work at their respective constant rates. How

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Machine R and machine S work at their respective constant rates. How  [#permalink]

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Machine R and machine S work at their respective constant rates. How much time does it take machine R, working alone, to complete a certain job?

(1) The amount of time that it takes machine S, working alone, to complete the job is 3/4 the amount of time that it takes machine R, working alone, to complete the job.
(2) Machine R and machine S, working together, take 12 minutes to complete the job.


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Re: Machine R and machine S work at their respective constant rates. How  [#permalink]

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New post 24 Jun 2018, 22:48
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Bunuel wrote:
Machine R and machine S work at their respective constant rates. How much time does it take machine R, working alone, to complete a certain job?

(1) The amount of time that it takes machine S, working alone, to complete the job is 34 the amount of time that it takes machine R, working alone, to complete the job.
(2) Machine R and machine S, working together, take 12 minutes to complete the job.


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(DS00858)


could you pls check the stat 1) , is it 34 the amount or 3/4th the amount or sumthin else , coz it is not clear the way it is stated
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Re: Machine R and machine S work at their respective constant rates. How  [#permalink]

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New post 24 Jun 2018, 23:00
doomedcat wrote:
Bunuel wrote:
Machine R and machine S work at their respective constant rates. How much time does it take machine R, working alone, to complete a certain job?

(1) The amount of time that it takes machine S, working alone, to complete the job is 34 the amount of time that it takes machine R, working alone, to complete the job.
(2) Machine R and machine S, working together, take 12 minutes to complete the job.


NEW question from GMAT® Official Guide 2019


(DS00858)


could you pls check the stat 1) , is it 34 the amount or 3/4th the amount or sumthin else , coz it is not clear the way it is stated

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Thank you. Edited.
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Machine R and machine S work at their respective constant rates. How  [#permalink]

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New post Updated on: 24 Jun 2018, 23:55
Bunuel wrote:
Machine R and machine S work at their respective constant rates. How much time does it take machine R, working alone, to complete a certain job?

(1) The amount of time that it takes machine S, working alone, to complete the job is 3/4 the amount of time that it takes machine R, working alone, to complete the job.
(2) Machine R and machine S, working together, take 12 minutes to complete the job.


NEW question from GMAT® Official Guide 2019


(DS00858)


let individual rates be R & S respectively, we need to find R

stat1 ) given that S = \(\frac{3}{4}\) R, but we do not more information to cal respective values , hence Not Suff

stat2) given together they both take 12 min , so lets put it the work time equation

\(\frac{1}{S}\)+\(\frac{1}{R}\) =\(1/12\) ==> \(\frac{R+X}{RS}\) = \(\frac{1}{12}\)

still not suff as we two unknowns and 1 eq

Stat1) + stat2) , we can use stat1) and put the value S in the eq of stat 2) , and we can cal R , Hence suff

C

Just for calculations, R= 28 mins
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Originally posted by doomedcat on 24 Jun 2018, 23:22.
Last edited by doomedcat on 24 Jun 2018, 23:55, edited 1 time in total.
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Re: Machine R and machine S work at their respective constant rates. How  [#permalink]

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New post 24 Jun 2018, 23:47
Let's assume R can do the work in r hrs. S can do the work in s hrs.
To find: s

From Statement 1:
\(r = \frac{3}{4} s\)
As, it is 2V 1E it is not solvable.
So, statement 1 is insufficient.

From Statement 2:
\(( \frac{1}{r} + \frac{1}{s}) \frac{12}{60} = 1\)
\(( \frac{1}{r} + \frac{1}{s}) = 5\)
As, it is 2V 1E it is not solvable.
So, statement 2 is insufficient.

From Statement 1 and Statement 2:
As we have 2V 2E we can solve it.
Hence, C is the correct answer.
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Re: Machine R and machine S work at their respective constant rates. How  [#permalink]

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New post 25 Jun 2018, 00:20
2

Solution



Given:
    • Machine R and machine S work at their respective constant rates

To find:
    • The time taken by machine R, working alone, to complete a certain job

Analysing Statement 1
    • As per the information given in statement 1, the amount of time that it takes machine S, working alone, to complete the job is \(\frac{3}{4}\) the amount of time that it takes machine R, working alone, to complete the job
    • From this statement, if we want to find out the time taken by R individually to complete the job, we must know the time taken by S individually to complete the job
      o As no information is given about the time taken by S to complete the job, we can’t find the time taken by R to complete the job

Hence, statement 1 is not sufficient to answer

Analysing Statement 2
    • As per the information given in statement 2, machine R and machine S, working together, take 12 minutes to complete the job
    • From this statement, if we want to find out the time taken by R to complete the job, we must know either the time taken by S to complete the job or their ratio of efficiency
      o As none of the information are provided, we cannot get the answer

Hence, statement 2 is not sufficient to answer

Combining Both Statements
Combining both the statements, we can write:
    • S takes \(\frac{3}{4}\) of the time taken by R to complete the job, while working alone
    • R and S together take 12 minutes to complete the job

If we assume R takes x minutes to complete the job, then S would have taken \(\frac{3x}{4}\) minutes to complete the job
    • Therefore, we can write \(\frac{1}{x} + \frac{4}{3x} = \frac{1}{12}\)
    • We can find the value of x from this given equation

Hence, the correct answer is option C.

Answer: C
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Re: Machine R and machine S work at their respective constant rates. How &nbs [#permalink] 25 Jun 2018, 00:20
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