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27 Dec 2023, 13:29
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E
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Difficulty:
65%
(hard)
Question Stats:
68% (02:44) correct
32%
(02:59)
wrong
based on 134
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Veronica and Trevor, working together but independently at their respective constant rates, can complete a certain job in less than 3 2/3 hours. Veronica, working by herself, can complete the job in 5 hours. If Trevor can complete the jobin t/2 hours , where t is an integer, what is the greatest possible value of t?
A. 23
B. 24
C. 25
D. 26
E. 27
A. 23
B. 24
C. 25
D. 26
E. 27
28 Dec 2023, 08:14
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Veronica and Trevor, working together but independently at their respective constant rates, can complete a certain job in less than 3 2/3 hours.
Rate * Time = Work Done
Since work done is same throughout the problem so lets take the work done as 1
Let Rate of Veronica = V
Rate of Trevor = T
If they work together then their combined rate will be = V + T
(V+T) * Time = 1
=> Time = \(\frac{1}{V+T}\) < 3\(\frac{2}{3}\)
=> \(\frac{1}{V+T}\) < \(\frac{3*3 + 2}{3}\)
=> \(\frac{1}{V+T}\) < \(\frac{11}{3}\)
=> V + T > \(\frac{3}{11}\) ...(1)
Veronica, working by herself, can complete the job in 5 hours
V * 5 = 1
=> V = \(\frac{1}{5}\)
Trevor can complete the job in t/2 hours , where t is an integer
=> T * \(\frac{t}{2}\) = 1
=> T = \(\frac{2}{t}\)
Substituting in (1) we get
\(\frac{1}{5}\) + \(\frac{2}{t}\) > \(\frac{3}{11}\)
=> \(\frac{2}{t}\) > \(\frac{3}{11}\) - \(\frac{1}{5}\)
=> \(\frac{2}{t}\) > \(\frac{3*5 - 1*11}{11*5}\)
=> \(\frac{2}{t}\) > \(\frac{4}{55}\)
=> t < \(\frac{55}{2}\)
=> t < 27.5
=> Max value of t = 27
So, Answer will be E
Hope it helps!
Watch the following video to MASTER Work Rate Problems
Rate * Time = Work Done
Since work done is same throughout the problem so lets take the work done as 1
Let Rate of Veronica = V
Rate of Trevor = T
If they work together then their combined rate will be = V + T
(V+T) * Time = 1
=> Time = \(\frac{1}{V+T}\) < 3\(\frac{2}{3}\)
=> \(\frac{1}{V+T}\) < \(\frac{3*3 + 2}{3}\)
=> \(\frac{1}{V+T}\) < \(\frac{11}{3}\)
=> V + T > \(\frac{3}{11}\) ...(1)
Veronica, working by herself, can complete the job in 5 hours
V * 5 = 1
=> V = \(\frac{1}{5}\)
Trevor can complete the job in t/2 hours , where t is an integer
=> T * \(\frac{t}{2}\) = 1
=> T = \(\frac{2}{t}\)
Substituting in (1) we get
\(\frac{1}{5}\) + \(\frac{2}{t}\) > \(\frac{3}{11}\)
=> \(\frac{2}{t}\) > \(\frac{3}{11}\) - \(\frac{1}{5}\)
=> \(\frac{2}{t}\) > \(\frac{3*5 - 1*11}{11*5}\)
=> \(\frac{2}{t}\) > \(\frac{4}{55}\)
=> t < \(\frac{55}{2}\)
=> t < 27.5
=> Max value of t = 27
So, Answer will be E
Hope it helps!
Watch the following video to MASTER Work Rate Problems
04 Nov 2025, 23:01
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
