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24 Jun 2018, 21:19
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
93% (01:06) correct
7%
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wrong
based on 2794
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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.
(DS00858)
(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)
20 Oct 2018, 06:19
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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!
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!
25 Jun 2018, 00:20
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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
