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Re: Time n Work Problem [#permalink]
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21 Nov 2013, 02:48
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? Please read the solution carefully: 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.
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Re: Time n Work Problem [#permalink]
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31 Dec 2013, 15:11
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
D is the correct answer
Hope this helps Cheers J
Last edited by jlgdr on 19 Feb 2014, 06:54, edited 1 time in total.



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Re: Time n Work Problem [#permalink]
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17 Jan 2014, 23:26
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 \(w=90\). \(\frac{w}{m}=6\). Answer: D. 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. thanks in advance



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Re: Time n Work Problem [#permalink]
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18 Jan 2014, 03:22
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 \(w=90\). \(\frac{w}{m}=6\). Answer: D. 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. thanks in advance 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: ittakes6daysfor3womenand2menworkingtogetherto82718.html#p751436Hope this helps.
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Re: Time n Work Problem [#permalink]
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18 Jan 2014, 03:55
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 \(w=90\). \(\frac{w}{m}=6\). Answer: D.[/quote] 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. thanks in advance[/quote] 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: ittakes6daysfor3womenand2menworkingtogetherto82718.html#p751436Hope 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.?



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Re: Time n Work Problem [#permalink]
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18 Jan 2014, 04:03



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Re: Time n Work Problem [#permalink]
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06 Feb 2014, 10:16
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 \(w=90\). \(\frac{w}{m}=6\). Answer: D. 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.



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Re: Time n Work Problem [#permalink]
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07 Feb 2014, 04:57
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 \(w=90\). \(\frac{w}{m}=6\). Answer: D. 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: ittakes6daysfor3womenand2menworkingtogetherto82718.html#p751436ittakes6daysfor3womenand2menworkingtogetherto8271820.html#p1272526ittakes6daysfor3womenand2menworkingtogetherto8271840.html#p1295389
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Re: It takes 6 days for 3 women and 2 men working together to [#permalink]
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16 Apr 2014, 01:51
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;



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Re: It takes 6 days for 3 women and 2 men working together to [#permalink]
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02 Sep 2014, 06:38
say if we express the first eqn in days then will the below eqn is fine . please correct me.
w/3 +m/2 = 6.



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Re: It takes 6 days for 3 women and 2 men working together to [#permalink]
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03 Sep 2014, 13:56
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?



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It takes 6 days for 3 women and 2 men working together to [#permalink]
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17 Oct 2014, 21:50
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 \(w=90\). \(\frac{w}{m}=6\). Answer: D. This is where i got my answer wrong: my equation is 3/m 9/w = 1/5



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Re: It takes 6 days for 3 women and 2 men working together to [#permalink]
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21 Oct 2014, 15:03
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.
Answer: D.
Bunnel, If men work 5 days less than women why are we adding 5 in equation 3/w? Dont we should minus 5 days ( t5).



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Re: It takes 6 days for 3 women and 2 men working together to [#permalink]
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21 Oct 2014, 15:06
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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 = d5



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Re: It takes 6 days for 3 women and 2 men working together to [#permalink]
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22 Oct 2014, 01:17
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.
Answer: D.
Bunnel, If men work 5 days less than women why are we adding 5 in equation 3/w? Dont we should minus 5 days ( t5). Please read this: ittakes6daysfor3womenand2menworkingtogetherto82718.html#p751436
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Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
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Re: It takes 6 days for 3 women and 2 men working together to [#permalink]
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12 Aug 2015, 07:01
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 answer is option (D) 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 x5 days that implies 1 w can complete 1/9x work in 1 day and 1 m can complete 1/(3x15) work in 1 day therefore, 12/(3x15) + 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.




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