Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 07 Feb 2016, 22:46

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# It takes 6 days for 3 women and 2 men working together to

Author Message
TAGS:
Math Expert
Joined: 02 Sep 2009
Posts: 31286
Followers: 5344

Kudos [?]: 62134 [1] , given: 9440

Re: Time n Work Problem [#permalink]  21 Nov 2013, 01:48
1
KUDOS
Expert's post
AccipiterQ wrote:
Bunuel wrote:
AndreG wrote:
Hm, i got stuck cuz I got something a little different:
YOURS: 3 men would do the same work 5 days sooner than 9 women --> $$\frac{m}{3}+5=\frac{w}{9}$$.

MINE: 3 men would do the same work 5 days sooner than 9 women --> $$\frac{3}{m}=\frac{9}{w}+5$$

In the above equation you also have for 2 men: $$\frac{2}{m}$$ - so why do u suddenly use the reciprocal? And why don't we add the 5 to women, because they take longer, hence their side is smaller...

Let one woman complete the job in $$w$$ days and one man in $$m$$ days.

First equation:
It takes 6 days for 3 women and 2 men working together to complete a work:
As the rate of 1 woman is $$\frac{1}{w}$$ job/day, then the rate of 3 women will be $$\frac{3}{w}$$ job/day. As the rate of 1 man is $$\frac{1}{m}$$ job/day, then the rate of 2 men will be $$\frac{2}{m}$$ job/day. Combined rate of 3 women and 2 men in one day will be: $$\frac{3}{w}+\frac{2}{m}$$ job/day.

As they do all the job in 6 days then in 1 day they do 1/6 of the job, which is combined rate of 3 women and 2 men --> $$\frac{3}{w}+\frac{2}{m}=\frac{1}{6}$$.

Second equation:
3 men would do the same work 5 days sooner than 9 women:
As 1 man needs $$m$$ days to do the job 3 men will need $$\frac{m}{3}$$ days to do the job. As 1 woman needs $$w$$ days to do the job 9 women will need $$\frac{w}{9}$$ days to do the job. 3 men would do the same work 5 days sooner means that 3 men will need 5 less days to do the job, hence $$\frac{m}{3}$$ is 5 less than $$\frac{w}{9}$$ --> $$\frac{m}{3}+5=\frac{w}{9}$$.

Hope it's clear.

My question is this, on the second equation how did you KNOW to put m/3, whereas in the first it was 2/m? In both cases aren't you figuring out the rate? In the first equation, you know that a man does 1/m of the job, and that 2 would do 2/m. In the second equation the rate is still 1/m, but you have 3 men, so should it not be 3/m+5=9/m?

First equation gives the rate: the rate of 1 man is $$\frac{1}{m}$$ job/day, then the rate of 2 men will be $$\frac{2}{m}$$ job/day.

Second equation gives time: 1 man needs $$m$$ days to do the job 3 men will need $$\frac{m}{3}$$ days to do the job.

Hope it's clear.
_________________
Current Student
Joined: 06 Sep 2013
Posts: 2036
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 39

Kudos [?]: 433 [0], given: 355

Re: Time n Work Problem [#permalink]  31 Dec 2013, 14:11
OK I think I think I found an easy algebraic solution to solve this one.

Let's begin with the second equation

W/9 - M/3 = 5

We have from here that w = 3m + 45
So we have that w = 3(m+15)

Now replace in the first equation 3/3(m+15) + 2/m = 1/6

The 3's cancel out and we are left with 1/(m+15)+2/m=1/6

We finally are left with a quadratic equation namely m^2 - 2m - 180. From here we have that m = 15

Replacing back in w= 3 (m+15) we have that w = 90.

So w/m = 90/15 = 6

Hope this helps
Cheers
J

Last edited by jlgdr on 19 Feb 2014, 05:54, edited 1 time in total.
Intern
Joined: 15 Jul 2012
Posts: 38
Followers: 0

Kudos [?]: 3 [0], given: 245

Re: Time n Work Problem [#permalink]  17 Jan 2014, 22:26
Bunuel wrote:
nonameee wrote:
Guys, even if you know the solution right away, it takes several minutes (definitely more than 3) to just write it down to find the answer. Is it a real GMAT question? Can something like that be expected on the real test?

Below is another solution which is a little bit faster.

It takes 6 days for 3 women and 2 men working together to complete a work.3 men would do the same work 5 days sooner than 9 women.How many times does the output of a man exceed that of a woman?
A. 3 times
B. 4 times
C. 5 times
D. 6 times
E. 7 times
Let one woman complete the job in $$w$$ days and one man in $$m$$ days. So the rate of 1 woman is $$\frac{1}{w}$$ job/day and the rate of 1 man is $$\frac{1}{m}$$ job/day.

It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: $$\frac{3}{w}+\frac{2}{m}=\frac{1}{6}$$.

3 men would do the same work 5 days sooner than 9 women --> $$\frac{m}{3}+5=\frac{w}{9}$$.

Solving: $$m=15$$ and $$w=90$$. $$\frac{w}{m}=6$$.

bunuel, pls help

if i equate time i am not getting it pls tell me where i am going wrong

lets take 1 woman can complete the work in 'w' days and 1 man can complete in 'm' days
so, it becomes w/3+m/2=6
and m/3+5=w/9

but i am getting the answer wrong.

Math Expert
Joined: 02 Sep 2009
Posts: 31286
Followers: 5344

Kudos [?]: 62134 [0], given: 9440

Re: Time n Work Problem [#permalink]  18 Jan 2014, 02:22
Expert's post
saggii27 wrote:
Bunuel wrote:
nonameee wrote:
Guys, even if you know the solution right away, it takes several minutes (definitely more than 3) to just write it down to find the answer. Is it a real GMAT question? Can something like that be expected on the real test?

Below is another solution which is a little bit faster.

It takes 6 days for 3 women and 2 men working together to complete a work.3 men would do the same work 5 days sooner than 9 women.How many times does the output of a man exceed that of a woman?
A. 3 times
B. 4 times
C. 5 times
D. 6 times
E. 7 times
Let one woman complete the job in $$w$$ days and one man in $$m$$ days. So the rate of 1 woman is $$\frac{1}{w}$$ job/day and the rate of 1 man is $$\frac{1}{m}$$ job/day.

It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: $$\frac{3}{w}+\frac{2}{m}=\frac{1}{6}$$.

3 men would do the same work 5 days sooner than 9 women --> $$\frac{m}{3}+5=\frac{w}{9}$$.

Solving: $$m=15$$ and $$w=90$$. $$\frac{w}{m}=6$$.

bunuel, pls help

if i equate time i am not getting it pls tell me where i am going wrong

lets take 1 woman can complete the work in 'w' days and 1 man can complete in 'm' days
so, it becomes w/3+m/2=6
and m/3+5=w/9

but i am getting the answer wrong.

That's because your equations are wrong. If one woman complete the job in $$w$$ days and one man in $$m$$ days, then w/3 is the time one woman needs to complete 1/3 of the work and m/2 is the time one man needs to complete 1/2 of the work. Adding them makes no sense. We can add rates but not times.

Check here: it-takes-6-days-for-3-women-and-2-men-working-together-to-82718.html#p751436

Hope this helps.
_________________
Intern
Joined: 15 Jul 2012
Posts: 38
Followers: 0

Kudos [?]: 3 [0], given: 245

Re: Time n Work Problem [#permalink]  18 Jan 2014, 02:55
Bunuel wrote:
Guys, even if you know the solution right away, it takes several minutes (definitely more than 3) to just write it down to find the answer. Is it a real GMAT question? Can something like that be expected on the real test?

Below is another solution which is a little bit faster.

It takes 6 days for 3 women and 2 men working together to complete a work.3 men would do the same work 5 days sooner than 9 women.How many times does the output of a man exceed that of a woman?
A. 3 times
B. 4 times
C. 5 times
D. 6 times
E. 7 times
Let one woman complete the job in $$w$$ days and one man in $$m$$ days. So the rate of 1 woman is $$\frac{1}{w}$$ job/day and the rate of 1 man is $$\frac{1}{m}$$ job/day.

It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: $$\frac{3}{w}+\frac{2}{m}=\frac{1}{6}$$.

3 men would do the same work 5 days sooner than 9 women --> $$\frac{m}{3}+5=\frac{w}{9}$$.

Solving: $$m=15$$ and $$w=90$$. $$\frac{w}{m}=6$$.

bunuel, pls help

if i equate time i am not getting it pls tell me where i am going wrong

lets take 1 woman can complete the work in 'w' days and 1 man can complete in 'm' days
so, it becomes w/3+m/2=6
and m/3+5=w/9

but i am getting the answer wrong.

That's because your equations are wrong. If one woman complete the job in $$w$$ days and one man in $$m$$ days, then w/3 is the time one woman needs to complete 1/3 of the work and m/2 is the time one man needs to complete 1/2 of the work. Adding them makes no sense. We can add rates but not times.

Check here: it-takes-6-days-for-3-women-and-2-men-working-together-to-82718.html#p751436

Hope this helps.[/quote]

oh silly me thanks for that quick response i always get confused with the reciprocality in rates and work. is there any other way to get hold of them.?
Math Expert
Joined: 02 Sep 2009
Posts: 31286
Followers: 5344

Kudos [?]: 62134 [0], given: 9440

Re: Time n Work Problem [#permalink]  18 Jan 2014, 03:03
Expert's post
saggii27 wrote:
oh silly me thanks for that quick response i always get confused with the reciprocality in rates and work. is there any other way to get hold of them.?

Please check the following post: new-project-review-discuss-and-get-kudos-points-153555.html#p1230606

Hope it helps.
_________________
Manager
Joined: 26 May 2013
Posts: 91
Followers: 0

Kudos [?]: 26 [0], given: 28

Re: Time n Work Problem [#permalink]  06 Feb 2014, 09:16
Bunuel wrote:
nonameee wrote:
Guys, even if you know the solution right away, it takes several minutes (definitely more than 3) to just write it down to find the answer. Is it a real GMAT question? Can something like that be expected on the real test?

Below is another solution which is a little bit faster.

It takes 6 days for 3 women and 2 men working together to complete a work.3 men would do the same work 5 days sooner than 9 women.How many times does the output of a man exceed that of a woman?
A. 3 times
B. 4 times
C. 5 times
D. 6 times
E. 7 times

Let one woman complete the job in $$w$$ days and one man in $$m$$ days. So the rate of 1 woman is $$\frac{1}{w}$$ job/day and the rate of 1 man is $$\frac{1}{m}$$ job/day.

It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: $$\frac{3}{w}+\frac{2}{m}=\frac{1}{6}$$.

3 men would do the same work 5 days sooner than 9 women --> $$\frac{m}{3}+5=\frac{w}{9}$$.

Solving: $$m=15$$ and $$w=90$$. $$\frac{w}{m}=6$$.

I stumbled on this answer and think it's worth clarifying:

In the second equation: 3 men would do the same work 5 days sooner than 9 women --> $$\frac{m}{3}+5=\frac{w}{9}$$.

m and w are representing TOTAL work done by men and women.

Whereas in the first equation: Let one woman complete the job in $$w$$ days and one man in $$m$$ days. So the rate of 1 woman is $$\frac{1}{w}$$ job/day and the rate of 1 man is $$\frac{1}{m}$$ job/day.

m and w are representing the RATE of work done by men and women.

I hope this is correct (Bunuel can you confirm?) and has helped some grasp the concept.
Math Expert
Joined: 02 Sep 2009
Posts: 31286
Followers: 5344

Kudos [?]: 62134 [0], given: 9440

Re: Time n Work Problem [#permalink]  07 Feb 2014, 03:57
Expert's post
mrwells2 wrote:
Bunuel wrote:
nonameee wrote:
Guys, even if you know the solution right away, it takes several minutes (definitely more than 3) to just write it down to find the answer. Is it a real GMAT question? Can something like that be expected on the real test?

Below is another solution which is a little bit faster.

It takes 6 days for 3 women and 2 men working together to complete a work.3 men would do the same work 5 days sooner than 9 women.How many times does the output of a man exceed that of a woman?
A. 3 times
B. 4 times
C. 5 times
D. 6 times
E. 7 times

Let one woman complete the job in $$w$$ days and one man in $$m$$ days. So the rate of 1 woman is $$\frac{1}{w}$$ job/day and the rate of 1 man is $$\frac{1}{m}$$ job/day.

It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: $$\frac{3}{w}+\frac{2}{m}=\frac{1}{6}$$.

3 men would do the same work 5 days sooner than 9 women --> $$\frac{m}{3}+5=\frac{w}{9}$$.

Solving: $$m=15$$ and $$w=90$$. $$\frac{w}{m}=6$$.

I stumbled on this answer and think it's worth clarifying:

In the second equation: 3 men would do the same work 5 days sooner than 9 women --> $$\frac{m}{3}+5=\frac{w}{9}$$.

m and w are representing TOTAL work done by men and women.

Whereas in the first equation: Let one woman complete the job in $$w$$ days and one man in $$m$$ days. So the rate of 1 woman is $$\frac{1}{w}$$ job/day and the rate of 1 man is $$\frac{1}{m}$$ job/day.

m and w are representing the RATE of work done by men and women.

I hope this is correct (Bunuel can you confirm?) and has helped some grasp the concept.

No, that's not correct.

m and w in both equations represent the same thing: time.

w is the number of days (time) one woman needs complete the job.
m is the number of days (time) one man needs complete the job.

The following posts might help:
it-takes-6-days-for-3-women-and-2-men-working-together-to-82718.html#p751436
it-takes-6-days-for-3-women-and-2-men-working-together-to-82718-20.html#p1272526
it-takes-6-days-for-3-women-and-2-men-working-together-to-82718-40.html#p1295389
_________________
Manager
Status: suffer now and live forever as a champion!!!
Joined: 01 Sep 2013
Posts: 149
Location: India
GPA: 3.5
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 44 [0], given: 75

Re: It takes 6 days for 3 women and 2 men working together to [#permalink]  16 Apr 2014, 00:51
one man can complete the work in m days.
(1/m)th of the work will completed per day.

women completes the work in n days.
(1/n)th of the work will be completed per day.
Their combined rate/day = 1/m + 1/n;

(1/m)th of the work will completed per day by one man.
??? ----------------------- by 3 man
(2/m)th of the work will be completed by 2 men /day
(1/n)th of the work will be completed per day by one woman/day.
??? --------------------------- by 3 women
(3/n)th of work will be completed by 3 women/day.
It takes 6 days for 3 women and 2 men working together to complete a work.
So, (1/6)th of the work will be completed by 3 women and 2 men working together per day.
2/m + 3/n = 1/6;

3 men would do the same work 5 days sooner than 9 women.
1 man needs m days to do the job 3 men will need m/3 days to do the job. As 1 woman needs n days to do the job
9 women will need n/9 days to do the same job.

3 men would do the same work 5 days sooner than 9 women.
m/3 +5 =n/9

m/n =6;
Hence D;
Manager
Joined: 07 Apr 2014
Posts: 147
Followers: 1

Kudos [?]: 19 [0], given: 81

Re: It takes 6 days for 3 women and 2 men working together to [#permalink]  02 Sep 2014, 05:38
say if we express the first eqn in days then will the below eqn is fine . please correct me.

w/3 +m/2 = 6.
Senior Manager
Joined: 07 Apr 2012
Posts: 464
Followers: 1

Kudos [?]: 33 [0], given: 58

Re: It takes 6 days for 3 women and 2 men working together to [#permalink]  03 Sep 2014, 12:56
Hi Guys.
Is there a way to do this without much time?
Some way to get to a good point to guess?
I saw IanStewart's post, but was wondering if someone has another idea?
Intern
Joined: 24 Jun 2014
Posts: 48
Followers: 0

Kudos [?]: 16 [0], given: 187

It takes 6 days for 3 women and 2 men working together to [#permalink]  17 Oct 2014, 20:50
Bunuel wrote:
nonameee wrote:
Guys, even if you know the solution right away, it takes several minutes (definitely more than 3) to just write it down to find the answer. Is it a real GMAT question? Can something like that be expected on the real test?

Below is another solution which is a little bit faster.

It takes 6 days for 3 women and 2 men working together to complete a work.3 men would do the same work 5 days sooner than 9 women.How many times does the output of a man exceed that of a woman?
A. 3 times
B. 4 times
C. 5 times
D. 6 times
E. 7 times

Let one woman complete the job in $$w$$ days and one man in $$m$$ days. So the rate of 1 woman is $$\frac{1}{w}$$ job/day and the rate of 1 man is $$\frac{1}{m}$$ job/day.

It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: $$\frac{3}{w}+\frac{2}{m}=\frac{1}{6}$$.

3 men would do the same work 5 days sooner than 9 women --> $$\frac{m}{3}+5=\frac{w}{9}$$.

Solving: $$m=15$$ and $$w=90$$. $$\frac{w}{m}=6$$.

This is where i got my answer wrong: my equation is 3/m -9/w = 1/5
Manager
Joined: 18 Jul 2013
Posts: 54
Followers: 0

Kudos [?]: 4 [0], given: 151

Re: It takes 6 days for 3 women and 2 men working together to [#permalink]  21 Oct 2014, 14:03
It takes 6 days for 3 women and 2 men working together to complete a work.3 men would do the same work 5 days sooner than 9 women.How many times does the output of a man exceed that of a woman?
A. 3 times
B. 4 times
C. 5 times
D. 6 times
E. 7 times

Let one woman complete the job in w days and one man in m days. So the rate of 1 woman is \frac{1}{w} job/day and the rate of 1 man is \frac{1}{m} job/day.

It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: \frac{3}{w}+\frac{2}{m}=\frac{1}{6}.

3 men would do the same work 5 days sooner than 9 women --> \frac{m}{3}+5=\frac{w}{9}.

Solving: m=15 and w=90. \frac{w}{m}=6.

Bunnel, If men work 5 days less than women why are we adding 5 in equation 3/w? Dont we should minus 5 days ( t-5).
Manager
Joined: 18 Jul 2013
Posts: 54
Followers: 0

Kudos [?]: 4 [0], given: 151

Re: It takes 6 days for 3 women and 2 men working together to [#permalink]  21 Oct 2014, 14:06
1
This post was
BOOKMARKED
Hi Bunnel,

I am a bit confuse here if men have taken 5 days less than whya re we adding 5 days, shouldn't we need to subtract 5 days.
Women time/day = d
Men time/day = d-5
Math Expert
Joined: 02 Sep 2009
Posts: 31286
Followers: 5344

Kudos [?]: 62134 [0], given: 9440

Re: It takes 6 days for 3 women and 2 men working together to [#permalink]  22 Oct 2014, 00:17
Expert's post
taleesh wrote:
It takes 6 days for 3 women and 2 men working together to complete a work.3 men would do the same work 5 days sooner than 9 women.How many times does the output of a man exceed that of a woman?
A. 3 times
B. 4 times
C. 5 times
D. 6 times
E. 7 times

Let one woman complete the job in w days and one man in m days. So the rate of 1 woman is \frac{1}{w} job/day and the rate of 1 man is \frac{1}{m} job/day.

It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: \frac{3}{w}+\frac{2}{m}=\frac{1}{6}.

3 men would do the same work 5 days sooner than 9 women --> \frac{m}{3}+5=\frac{w}{9}.

Solving: m=15 and w=90. \frac{w}{m}=6.

Bunnel, If men work 5 days less than women why are we adding 5 in equation 3/w? Dont we should minus 5 days ( t-5).

_________________
Manager
Joined: 10 Jun 2015
Posts: 128
Followers: 1

Kudos [?]: 17 [0], given: 0

Re: It takes 6 days for 3 women and 2 men working together to [#permalink]  12 Aug 2015, 06:01
virtualanimosity wrote:
It takes 6 days for 3 women and 2 men working together to complete a work. 3 men would do the same work 5 days sooner than 9 women. How many times does the output of a man exceed that of a woman?

A. 3 times
B. 4 times
C. 5 times
D. 6 times
E. 7 times

2m and 3w can do a work in 6 days or 12m and 18w in 1 day
let 9 w take x days, then 3 m will take x-5 days
that implies 1 w can complete 1/9x work in 1 day and 1 m can complete 1/(3x-15) work in 1 day
therefore, 12/(3x-15) + 18/9x = 1
solving we get x = 1 or 10
x does not take the value 1
so, 1m can do the work in 15 days and 1 w does the same work in 90 days.
Re: It takes 6 days for 3 women and 2 men working together to   [#permalink] 12 Aug 2015, 06:01

Go to page   Previous    1   2   3   [ 56 posts ]

Similar topics Replies Last post
Similar
Topics:
1 The ratio of men to women in a class is 6 to 5. If 2 men and 1 woman 9 03 Jan 2016, 11:15
1 The ratio of men to women at a banquet is 6:5. If ten men leave the pa 1 12 Sep 2015, 11:48
2 3 men and 3 women need to be seated in 2 rows with 3 chairs 5 28 Sep 2010, 05:47
6 A work crew of 4 Men takes 5 days to complete one-half of a 10 13 Mar 2010, 08:24
14 It takes 6 days for 3 women and 2 men working together to 13 12 Mar 2010, 22:33
Display posts from previous: Sort by