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

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

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

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

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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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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Lowkya wrote:
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:
$$r = \frac{3}{4} s$$

Don't you think it should be
$$s = \frac{3}{4} r$$

Kind Regards!
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Re: Machine R and machine S work at their respective constant rates. How [#permalink]
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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 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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(DS00858)

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

Solution:

Question Stem Analysis:

We need to determine the amount of time it takes machine R to complete a certain job alone.

Statement One Alone:

From statement one, we see that machine R takes 4/3 the amount of time of machine S to complete the job alone. However, without knowing the amount of time it takes machine S to complete the job alone, we can’t determine the amount of time it takes marchine R to complete the job alone. Statement one alone is not sufficient.

Statement Two Alone:

Knowing that it takes 12 minutes for machine R and machine S, combined, to complete the job is not sufficient to ascertain the amount of time it takes for machine R to complete the job alone. Statement two alone is not sufficient.

Statements One and Two Together:

If we let x be the amount of time (in minutes) it takes machine R to complete the job alone, then its rate is 1/x. We know it takes machine S4/3 the time it takes machine R, so its time is 4x/3 minutes, and its rate is 1/(4x/3). Since it takes them 12 minutes to complete the job when working together, we can create the rate equation:

1/x + 1/(4x/3) = 1/12

Without actually solving the equation, we see that we can determine a value for x. The two statements together are sufficient.

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