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Working together, Rafael and Salvador can tabulate a certain set of da

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Working together, Rafael and Salvador can tabulate a certain set of da  [#permalink]

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New post 03 Aug 2018, 10:35
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Working together, Rafael and Salvador can tabulate a certain set of data in 2 hours. In how many hours can Rafael tabulate the data working alone?

(1) Working alone, Rafael can tabulate the data in 3 hours less time than Salvador, working alone, can tabulate the data.
(2) Working alone, Rafael can tabulate the data in 1/2 the time that Salvador, working alone, can tabulate the data.


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(DS13907)

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Re: Working together, Rafael and Salvador can tabulate a certain set of da  [#permalink]

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New post 03 Aug 2018, 13:39
Bunuel wrote:
Working together, Rafael and Salvador can tabulate a certain set of data in 2 hours. In how many hours can Rafael tabulate the data working alone?

(1) Working alone, Rafael can tabulate the data in 3 hours less time than Salvador, working alone, can tabulate the data.
(2) Working alone, Rafael can tabulate the data in 1/2 the time that Salvador, working alone, can tabulate the data.


NEW question from GMAT® Quantitative Review 2019


(DS13907)


Let 'r' and 's' are the no of hours taken by Rafael & Salvador, working alone, to complete the job respectively.

Given, \(\frac{1}{r}+\frac{1}{s}=\frac{1}{2}\)-------------(1)

Question stem:- r=?

St1:- Working alone, Rafael can tabulate the data in 3 hours less time than Salvador, working alone, can tabulate the data.
Or, r=s-3 Or, s=r+3
from(1), we have, \(\frac{1}{r}+\frac{1}{s}=\frac{1}{2}\)
Now substituting, \(\frac{1}{r}+\frac{1}{(r+3)}=\frac{1}{2}\)
Or, \(r^2-r-6=0\)
Or, (r+2)(r-3)=0
Or, r=3
Sufficient.

St2:- Working alone, Rafael can tabulate the data in 1/2 the time that Salvador, working alone, can tabulate the data.
Or, \(r=\frac{s}{2}\) Or, \(s=2r\)
from(1), we have, \(\frac{1}{r}+\frac{1}{s}=\frac{1}{2}\)
Now substituting, \(\frac{1}{r}+\frac{1}{2r}=\frac{1}{2}\)
Or, 2r=6
Or, r=3
Sufficient.

Ans. (D)
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Re: Working together, Rafael and Salvador can tabulate a certain set of da &nbs [#permalink] 03 Aug 2018, 13:39
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