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

Question

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.

(DS00858)

JeffYin · Accepted Answer

Even though this is a relatively easy question, it gives us the opportunity to practice a number of my GMAT timing tips (the links below include growing lists of questions that you can use to practice each tip):

Rate problems: Use D = R x T and W = R x T  
In statement 2, we can write W = Rc * Tc, where Rc is the combined rate and Tc is the combined time. We could even just write 12 in the place of Tc, because we are given the combined time.

Set the amount of work equal to 1 for a single job  
In the above equation, we can just set W = 1 because we are talking about completing a single job.

Add rates when they are simultaneous  
If Rr and Rs are the rates of machines R and S, respectively, then the combined rate Rc = Rr + Rs. because the machines are working together simultaneously.

Rate and time are reciprocals of each other for a single job  
Notice that we are solving for the time it takes machine R to do the job alone. Let's call this Tr, and call the time it takes machine S to do the job alone Ts. Because we're talking about completing a single job, rate and time are reciprocals of each other, so Rr = 1/Tr and Rs = 1/Ts.

Check quickly if two answers are possible on Data Sufficiency questions  
If we plug all of the above back into our W = Rc * Tc equation, we get 1 = (1/Tr + 1/Ts) * 12. While we may not easily come up with values for Tr and Ts that satisfy this equation, we still might pretty quickly see that multiple values are possible for Tr (we could easily plug in two different values for Tr that are larger than 12, and we would be able to solve for a Ts in each case that would satisfy the equation). Similarly, for the equation that comes from statement 1 (Ts = 3/4 * Tr), for any value of Tr, we could come up with a value of Ts that works, so multiple possible values are possible for Tr.

Only do math until you see you can get an answer on Data Sufficiency questions  
Once we get around to combining the equations for the 2 statements, the math could get messy. However, if we stop once we realize that we have a single equation with Tr, and that this is in a form where only 1 value of Tr is possible, then we don't take any more time than is needed to see that both statements are sufficient together.

Please let me know if you have any questions, or if you want me to post a video solution!

EgmatQuantExpert · Answer

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

doomedcat · Answer

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

Bunuel · Answer

________________________
Thank you. Edited.

doomedcat · Answer

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

Lowkya · Answer

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.

Radheya · Answer

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

Kind Regards!

GMATinsight · Answer

Answer: Option C

Video solution by  GMATinsight

https://www.youtube.com/watch?v=gnQd6wOe9Vk

ScottTargetTestPrep · Answer

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.

Answer: C

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=q6HfRsEiKjQ

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