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
Attachments
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