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18 Mar 2013, 09:45
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
54% (02:52) correct
46%
(02:54)
wrong
based on 270
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Raghavachari, Viswanathan and Venkatraman together finished 4/5 th of a certain task . Had only Raghavachari and Viswanathan worked on the task, it would have taken 20 days to complete that part of the task. If Venkatraman is the fastest of the three workers, which of the following could be the total number of days taken to complete the whole task assuming all the three work together throughout?
A. 16
B. 18
C. 20
D. 22
E. 24
A. 16
B. 18
C. 20
D. 22
E. 24
18 Mar 2013, 10:40
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I found this exercise too complex to be a real GMAT problem.
For simplicity
, let's call them Rag, Vis & Ven.
We know Rag and Vis working together spend 20 days for 4/5 of the job --> this means 25 days for the entire job, Rag and Vis working together, at that pace. (1)
And we have the formula used for work problems: the entire job time T, with the three guys working together, will be (2):
\(\frac{1}{T}=\frac{1}{Rag}+\frac{1}{Vis}+\frac{1}{Ven}\)
where: Rag is the time Rag needs to complete the work alone, Vis is the time Vis needs to complete the work alone, and Ven is the time Ven needs to complete the work alone.
Now, because of (1), we know that (3):
\(\frac{1}{25}=\frac{1}{Rag}+\frac{1}{Vis}\)
Therefore, we can substitute (3) on (2), to get (4):
\(\frac{1}{T}=\frac{1}{25}+\frac{1}{Ven}\)
Now, it said that Ven is faster that the other guys with long names.
This was the difficult part for me: if Rag and Vis can do the entire work in 25 days, reordering (3) this means that (5):
\(25=\frac{Rag*Vis}{Rag+Vis}\)
There are at least 5 options for this to be 25 (see attached graph):
Rag=50 and Vis=50
Rag=30 and Vis=150
Rag=26 and Vis=650
Rag=150 and Vis=30
Rag=650 and Vis=26.
But we have to analyze to choices they give us. We get (4) and solve for Ven depending on T (6):
\(Ven=\frac{25*T}{25-T}\)
If we plug T=16 (option A), we get that Ven=44 days approx.
If we plug T=18 (option B), we get that Ven=64 days approx.
If we plug T=20 (option C), we get that Ven=100 days approx. and so on
With the choices we are given, and knowing that Ven has to be the fast guy, we can only opt for the answer A, assuming that Rag and Vis take each 50 days to complete the task by their own.
Answer A
For simplicity
, let's call them Rag, Vis & Ven.We know Rag and Vis working together spend 20 days for 4/5 of the job --> this means 25 days for the entire job, Rag and Vis working together, at that pace. (1)
And we have the formula used for work problems: the entire job time T, with the three guys working together, will be (2):
\(\frac{1}{T}=\frac{1}{Rag}+\frac{1}{Vis}+\frac{1}{Ven}\)
where: Rag is the time Rag needs to complete the work alone, Vis is the time Vis needs to complete the work alone, and Ven is the time Ven needs to complete the work alone.
Now, because of (1), we know that (3):
\(\frac{1}{25}=\frac{1}{Rag}+\frac{1}{Vis}\)
Therefore, we can substitute (3) on (2), to get (4):
\(\frac{1}{T}=\frac{1}{25}+\frac{1}{Ven}\)
Now, it said that Ven is faster that the other guys with long names.
This was the difficult part for me: if Rag and Vis can do the entire work in 25 days, reordering (3) this means that (5):
\(25=\frac{Rag*Vis}{Rag+Vis}\)
There are at least 5 options for this to be 25 (see attached graph):
Rag=50 and Vis=50
Rag=30 and Vis=150
Rag=26 and Vis=650
Rag=150 and Vis=30
Rag=650 and Vis=26.
But we have to analyze to choices they give us. We get (4) and solve for Ven depending on T (6):
\(Ven=\frac{25*T}{25-T}\)
If we plug T=16 (option A), we get that Ven=44 days approx.
If we plug T=18 (option B), we get that Ven=64 days approx.
If we plug T=20 (option C), we get that Ven=100 days approx. and so on
With the choices we are given, and knowing that Ven has to be the fast guy, we can only opt for the answer A, assuming that Rag and Vis take each 50 days to complete the task by their own.
Answer A
Attachments
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19 Mar 2013, 01:18
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Solution:
Let us call the three men as R, VI and VE
1) Time taken by R and VI to complete 4/5 of the task is 20 days
2) VE is the fastest of the three workers
3) From (1), Time that would be taken by R and VI to complete the whole task is 25 days
4) We may assume that R and VI take 50 days each to complete the task
5) From (2) and (4) we have VE taking less than 50 days or \(1/VE > 1/50\)
6) From (4) and (5), we have , \(1/Total time = 1/R + 1/VI + 1/VE > 1/50 + 1/50+ 1/50\)
or\(1/ Total Time\) > 3/50 or Total time taken < 16.67 days.
The only choice that fits the above value is choice A.
Note: The number of days taken to complete the task cannot be greater than the above because VE being the fastest worker the maximum number of days that VE could possibly take is 49. Lesser values would lessen the total time taken.
