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Working at their respective constant rates, Paul, Abdul and Adam alone
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30 Apr 2021, 05:26
30 Apr 2021, 05:26
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Question Stats:
48% (02:08) correct
51% (02:26) wrong based on 47 sessions
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Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction of the work will be done by Adam?
(A) 1/4
(B) 12/47
(C) 1/3
(D) 5/12
(E) 20/47
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
(A) 1/4
(B) 12/47
(C) 1/3
(D) 5/12
(E) 20/47
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Working at their respective constant rates, Paul, Abdul and Adam alone
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30 Apr 2021, 05:36
30 Apr 2021, 05:36
2
Work done by Paul per hour = \(\frac{1}{3}\)
Work done by Abdul per hour = \(\frac{1}{4}\)
Work done by Adam per hour = \(\frac{1}{5}\)
Total work done per hour = \(\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\)
= \(\frac{20+15+12}{60}\)
= \(\frac{47}{60}\)
Total work done = \(\frac{60}{47}\)
Fraction of work done by Adam = \(\frac{60}{47} * \frac{1}{5}\)
= \(\frac{12}{47 }\)
Hence, B
Work done by Abdul per hour = \(\frac{1}{4}\)
Work done by Adam per hour = \(\frac{1}{5}\)
Total work done per hour = \(\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\)
= \(\frac{20+15+12}{60}\)
= \(\frac{47}{60}\)
Total work done = \(\frac{60}{47}\)
Fraction of work done by Adam = \(\frac{60}{47} * \frac{1}{5}\)
= \(\frac{12}{47 }\)
Hence, B
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Re: Working at their respective constant rates, Paul, Abdul and Adam alone
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30 Apr 2021, 05:41
30 Apr 2021, 05:41
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Carcass wrote:
Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction of the work will be done by Adam?
(A) 1/4
(B) 12/47
(C) 1/3
(D) 5/12
(E) 20/47
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
(A) 1/4
(B) 12/47
(C) 1/3
(D) 5/12
(E) 20/47
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
One approach is to assign a "nice" value to the entire job. That is, a value that works well with the given information (3, 4, and 5 hours).
The least common multiple of 3, 4 and 5 is 60.
So, let's say the ENTIRE job consists of making 60 widgets.
If Paul can complete the job (make 60 widgets) in 3 hours, then his RATE of work = 20 widgets PER HOUR
If Abdul can make 60 widgets in 4 hours, then his RATE of work = 15 widgets PER HOUR
If Adam can make 60 widgets in 5 hours, then his RATE of work = 12 widgets PER HOUR
So, if they work TOGETHER, their combined RATE = 20 + 15 + 12 = 47 widgets PER HOUR
So, for every HOUR that passes, the GROUP can make 47 widgets
We also know that, for every HOUR that passes, the Adam can made 12 widgets (since his RATE of work = 12 widgets PER HOUR)
This means that, when the 3 people work together, Adam makes 12/47 of the widgets
Answer: B
Cheers,
Brent
