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Math Expert V
Joined: 02 Sep 2009
Posts: 58434
Working together, Rafael and Salvador can tabulate a certain set of da  [#permalink]

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27 00:00

Difficulty:   25% (medium)

Question Stats: 72% (01:35) correct 28% (02:02) wrong based on 682 sessions

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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.

NEW question from GMAT® Quantitative Review 2019

(DS13907)

_________________
VP  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1013
WE: Supply Chain Management (Energy and Utilities)
Re: Working together, Rafael and Salvador can tabulate a certain set of da  [#permalink]

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5
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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PKN

Rise above the storm, you will find the sunshine
General Discussion
Intern  Joined: 09 Jan 2019
Posts: 2
Re: Working together, Rafael and Salvador can tabulate a certain set of da  [#permalink]

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How did you transform $$\frac{1}{(r+3)}+\frac{1}{r}=\frac{1}{2}$$ into $$r^2-r-6=0$$ ? PKN VP  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1013
WE: Supply Chain Management (Energy and Utilities)
Re: Working together, Rafael and Salvador can tabulate a certain set of da  [#permalink]

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redwood wrote:
How did you transform $$\frac{1}{(r+3)}+\frac{1}{r}=\frac{1}{2}$$ into $$r^2-r-6=0$$ ? PKN Hi redwood,
You must know the addition and subtraction of fractional expressions.

Here, $$\frac{1}{(r+3)}+\frac{1}{r}=\frac{1}{2}$$

Or, $$\frac{[1*r+1*(r+3)]}{(r+3)r}=\frac{1}{2}$$
Or, $$\frac{(2r+3)}{(r^2+3r)}=\frac{1}{2}$$
Cross-multiplying, We have
$$2(2r+3)=r^2+3r$$
Or, $$4r+6=r^2+3r$$
Or, $$r^2-r-6=0$$

Hope it helps.
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Intern  Joined: 09 Jan 2019
Posts: 2
Re: Working together, Rafael and Salvador can tabulate a certain set of da  [#permalink]

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PKN Thanks a lot, got it now! Intern  B
Joined: 14 Sep 2018
Posts: 11
Schools: MIT SDM "20 (D)
Re: Working together, Rafael and Salvador can tabulate a certain set of da  [#permalink]

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1
Thanks. OG had a very confusing explanation. This is quite clear, and straightforward to follow.
Target Test Prep Representative P
Status: Chief Curriculum and Content Architect
Affiliations: Target Test Prep
Joined: 24 Nov 2014
Posts: 618
GMAT 1: 800 Q51 V51 Re: Working together, Rafael and Salvador can tabulate a certain set of da  [#permalink]

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2
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.

Information given:

Working together, Rafael and Salvador can tabulate a certain set of data in 2 hours.

Question:

In how many hours can Rafael tabulate the data working alone?

This question may seem complicated, but the truth is that since we know how long it takes for the two of them to complete the job, if we have any information that we can use to accurately compare how fast one works to how fast the other works, then we can answer the question.

Statement 1: Working alone, Rafael can tabulate the data in 3 hours less time than Salvador, working alone, can tabulate the data.

We do not need to use any math to determine whether this statement is sufficient. We have only to notice that we know how long it takes for both of them to do the work together and that we have information that we can use to determine their relative speeds. With that information, we could work our way to the answer to the question, how many hours Rafael would take to do the job alone.

To see why, consider this:

Time for Rafael to do the job = R

Time for Salvador to do the job = R + 3

We are now working with one variable, and we have the time it takes for them to do the job together. So, we could work our way to Rafael's time.

Sufficient.

Statement 2: Working alone, Rafael can tabulate the data in 1/2 the time that Salvador, working alone, can tabulate the data.

This tells us that Rafael works twice as fast as Salvador works. Since we know how long they take to do the job together, we can clearly work our way to Rafael's speed and then his time to do the job himself.

To see why, consider this:

Rafael's speed = 1/r

Salvador's speed = 1/2r

We are now working with one variable, and we have the time it takes for them to do the job together. So, we could work our way to Rafael's time, but we won't because this is a DS question.

Sufficient.

The correct answer is D.
_________________

Marty Murray

Chief Curriculum and Content Architect

Marty@targettestprep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

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Intern  B
Joined: 04 Jun 2014
Posts: 15
Re: Working together, Rafael and Salvador can tabulate a certain set of da  [#permalink]

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Hi Marty,

I've solved this with similar logic and didn't solve the equation. Although, I knew that this equation will come out to be a quadratic which might have both imaginary roots or 2 positive roots.
So, my question is about the assumption that Gmat will give a true scenario in statements which will for sure have one positive root only that will be an answer. Thus, we don't need to check if the equation has only 1 positive root.
Please, let me know if this assumption is wrong.

Regards,
Pankaj

MartyTargetTestPrep wrote:
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.

Information given:

Working together, Rafael and Salvador can tabulate a certain set of data in 2 hours.

Question:

In how many hours can Rafael tabulate the data working alone?

This question may seem complicated, but the truth is that since we know how long it takes for the two of them to complete the job, if we have any information that we can use to accurately compare how fast one works to how fast the other works, then we can answer the question.

Statement 1: Working alone, Rafael can tabulate the data in 3 hours less time than Salvador, working alone, can tabulate the data.

We do not need to use any math to determine whether this statement is sufficient. We have only to notice that we know how long it takes for both of them to do the work together and that we have information that we can use to determine their relative speeds. With that information, we could work our way to the answer to the question, how many hours Rafael would take to do the job alone.

To see why, consider this:

Time for Rafael to do the job = R

Time for Salvador to do the job = R + 3

We are now working with one variable, and we have the time it takes for them to do the job together. So, we could work our way to Rafael's time.

Sufficient.

Statement 2: Working alone, Rafael can tabulate the data in 1/2 the time that Salvador, working alone, can tabulate the data.

This tells us that Rafael works twice as fast as Salvador works. Since we know how long they take to do the job together, we can clearly work our way to Rafael's speed and then his time to do the job himself.

To see why, consider this:

Rafael's speed = 1/r

Salvador's speed = 1/2r

We are now working with one variable, and we have the time it takes for them to do the job together. So, we could work our way to Rafael's time, but we won't because this is a DS question.

Sufficient.

The correct answer is D.
Target Test Prep Representative P
Status: Chief Curriculum and Content Architect
Affiliations: Target Test Prep
Joined: 24 Nov 2014
Posts: 618
GMAT 1: 800 Q51 V51 Working together, Rafael and Salvador can tabulate a certain set of da  [#permalink]

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pankajpaliitkgp wrote:
Hi Marty,

I've solved this with similar logic and didn't solve the equation. Although, I knew that this equation will come out to be a quadratic which might have both imaginary roots or 2 positive roots.
So, my question is about the assumption that Gmat will give a true scenario in statements which will for sure have one positive root only that will be an answer. Thus, we don't need to check if the equation has only 1 positive root.
Please, let me know if this assumption is wrong.

Regards,
Pankaj

Hi Pahkaj.

If a problem Solving question could be solved via the use of a quadratic, the solution will have only one root that works. Of course, Problem Solving questions have to work that way. Otherwise, they would not make sense, as a problem solving question has to have only one correct answer.

However, in answering a Data Sufficiency question, you can't assume that there will be only one root that works. It could be that there are multiple roots that work and that a statement or both statements are, therefore, insufficient.
_________________

Marty Murray

Chief Curriculum and Content Architect

Marty@targettestprep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Working together, Rafael and Salvador can tabulate a certain set of da   [#permalink] 28 Mar 2019, 08:46
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