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)
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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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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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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!
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