Oct 18 08:00 AM PDT  09:00 AM PDT Learn an intuitive, systematic approach that will maximize your success on Fillintheblank GMAT CR Questions. Oct 19 07:00 AM PDT  09:00 AM PDT Does GMAT RC seem like an uphill battle? eGMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss!
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 19 Aug 2009
Posts: 77

It takes 6 days for 3 women and 2 men working together to
[#permalink]
Show Tags
Updated on: 04 Jul 2013, 08:11
Question Stats:
35% (03:05) correct 65% (03:12) wrong based on 964 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by virtualanimosity on 19 Aug 2009, 13:33.
Last edited by Bunuel on 04 Jul 2013, 08:11, edited 2 times in total.
Edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 58402

Re: Time n Work Problem
[#permalink]
Show Tags
19 Jul 2010, 10:44
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.
_________________




Manager
Joined: 14 Feb 2011
Posts: 144

Re: Time n Work Problem
[#permalink]
Show Tags
06 Mar 2011, 10:42
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? 1] 3 times 2] 4 times 3] 5 times 4] 6 times 5] 7 times Let women do \(w\) units of work per day and men do \(m\) units of work per day, then question asks, what is m/w Total units of work to be done = \(6*(3*w+2*m)\) Time taken by 9 women to do this work on their own = \(6*(3*w+2*m)\)/\((9*w)\) = \(2 + 4/3*m/w\) Time taken by 3 men to do this work on their own = \(6*(3*w+2*m)/(3*m)\) = \(6/(m/w) + 4\) Let m/w be x then we know \(2 + (4/3)*x 6/x 4 = 5\) or \((4/3)*x  6/x= 7\) Now substituting for x from choices will quickly give us x = 6 so D I like this as it reduces quickly to the required form of m/w and it obviates the need for a quadratic equation and also lest w and m remain in numerator most of the time




Director
Joined: 16 Jul 2009
Posts: 779
Schools: CBS
WE 1: 4 years (Consulting)

Re: Time n Work Problem
[#permalink]
Show Tags
19 Aug 2009, 16:00
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? 1] 3 times 2] 4 times 3] 5 times 4] 6 times 5] 7 times Clear D: x: days 9 women doing the job > 1 woman works W=1/9x per day x5: days 3 men doing the job > 1 man works M=1/[3*(x5)] per day The answer to the question is: M/W And, how much is x? As per first data: 2*M+3*W=1/6 You can solve x, and obtain 2 values, 10 and 1 (1 is impossible because that would imply that the 3 men take 4 days), so x=10. So M/W=6 times
_________________



Director
Joined: 23 Apr 2010
Posts: 507

Re: Time n Work Problem
[#permalink]
Show Tags
19 Jul 2010, 01:10
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?



Intern
Joined: 22 Jun 2010
Posts: 37

Re: Time n Work Problem
[#permalink]
Show Tags
19 Jul 2010, 13:05
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. 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...



Math Expert
Joined: 02 Sep 2009
Posts: 58402

Re: Time n Work Problem
[#permalink]
Show Tags
19 Jul 2010, 13:25
AndreG 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. 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.
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 58402

Re: Time n Work Problem
[#permalink]
Show Tags
22 Jul 2010, 04:28
sam2010 wrote: BunelI got a quadratic equation while solving these two eqn. Is there a simple way of solving them? I also got quadratic equation (\(m^23m180=0\)) and it wasn't too hard to solve (discriminant would be perfect square \(d=3^3+4*180=729=27^2\)) > \(m=12\) or \(m=15\).
_________________



Intern
Joined: 22 Dec 2010
Posts: 6

Re: Time n Work Problem
[#permalink]
Show Tags
24 Jan 2011, 10:20
First set : 3/w+2/m=1/6 Second set: 3/m = 1/x and 9/w=1/(x+5) ==> 1/m = 1/3x and 1/w = 1/9(x+5) Enter in first equation and solve for x 1/(3x+15) + 2/3x = 1/6 simplify => x^2x20=0 solve for x : x=(1 + (1+80)^,5)/2= (1+ 9)/2. X can only be positive ==> x= 5 enter in 2nd set ==> 3/m=1/5 and 9/w=1/10 => 3/2m=9/w => m/w=1/6



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1806

Re: Time n Work Problem
[#permalink]
Show Tags
06 Mar 2011, 22:08
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? 1] 3 times 2] 4 times 3] 5 times 4] 6 times 5] 7 times I received a PM asking me to respond. First, this is definitely not a realistic GMAT question. For one thing, it's horribly written (the phrase 'to complete a work' is not English, the question should read '*By* how many times...', the question needs to make clear that each man works at the same rate, as does each woman, the word 'sooner' is nonidiomatic, the word 'output' is misused, etc). For another, it's terribly contrived, and altogether tedious if you take any normal approach; I don't see any direct way to solve that will allow you to avoid a quadratic equation. Real GMAT questions are never designed in such a way, so you can confidently move on to better material and ignore this question (incidentally, where is it from?). While it isn't especially fast either, you can work backwards from the answers here relatively easily. This might at least be less confusing for some than a direct (algebraic) approach. Say we get 1 unit of work per woman per day. If you test, say, answer C, we'd then get 5 units of work per man per day. The job would then require 6(3 + 2*5) = 78 units of work. Notice that, to find how long it will take 9 women to do the job, we'll need to get an integer when we divide 78 by 9, so C cannot be right. If you move next to D, we have 6 units of work per man per day, and the job requires 6(3 + 2*6) = 90 units of work. Thus 9 women do the job in 10 days, and 3 men would do the job in 90/(6*3) = 5 days, so D is correct.
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com



Director
Joined: 22 Mar 2011
Posts: 588
WE: Science (Education)

Re: It takes 6 days for 3 women and 2 men working together to
[#permalink]
Show Tags
15 Sep 2012, 11:53
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 The fastest and easiest way to solve this question was already proposed by IanStewart. I am trying another algebraic approach. Denote by \(W\) the rate of a woman, by \(M\) that of a men, and by \(T\) the time it takes 9 women to complete the work. We have the following equations: \(6(3W + 2M) = 9WT = 3M(T5)\), or, after reducing by 3, \(2(3W + 2M) = 3WT = M(T  5).\) We are looking for the ratio \(M/W\) which we can denote by \(n.\) Substituting in the above equations \(M = nW,\) we can write: \(2(3W + 2nW) = 3WT = nW(T  5).\) Divide through by \(W,\) so \(6 + 4n = 3T = nT  5n.\) Solving for \(T\) (equality between the last two expressions) we obtain \(T=\frac{5n}{n3}.\) Taking the equality of the first two expressions, we get \(6+4n=\frac{3\cdot{5}n}{n3}.\) From the possible answer choices we can deduce that \(n\) must be a positive integer. We need \(\frac{15n}{n3}\) to be a positive integer. We can see that \(n\) cannot be odd and it must be greater than 3. We have to choose between B and D. Only \(n = 6\) works. Answer D.
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Senior Manager
Joined: 24 Mar 2010
Posts: 335

Re: Time n Work Problem
[#permalink]
Show Tags
19 Sep 2012, 15:56
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. How did you solve for m and w in the very last part? I do the algebra and can't get the right answer. You have one equation with 2 unknown variables.



Director
Joined: 22 Mar 2011
Posts: 588
WE: Science (Education)

Re: Time n Work Problem
[#permalink]
Show Tags
19 Sep 2012, 23:39
Shawshank 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. How did you solve for m and w in the very last part? I do the algebra and can't get the right answer. You have one equation with 2 unknown variables. You have 2 equations with two unknowns: First equation \(\frac{3}{w}+\frac{2}{m}=\frac{1}{6}.\) Second equation \(\frac{m}{3}+5=\frac{w}{9}\). After getting rid of the denominators (multiply first equation by \(6wm\) and the second by 9), for example express \(w\) from the second equation and substitute it into the first. You obtain a quadratic equation for \(m\): \(m^23m180=0\) This equation has one positive and one negative root. The sum of the two roots must be 3 and their product 180. Using factorization for 180, you can find 12 and 15. So \(m=15\) and \(w=90.\) For another algebraic approach see: ittakes6daysfor3womenand2menworkingtogetherto82718.html#p1121807
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Senior Manager
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 445
Location: India
GMAT 1: 710 Q50 V36 GMAT 2: 750 Q51 V41 GMAT 3: 790 Q51 V49
GPA: 3.3

Re: Time n Work Problem
[#permalink]
Show Tags
30 Sep 2013, 01:44
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. Can you please help me to understand on what logic did you make this explanation 3 men would do the same work 5 days sooner than 9 women > \(\frac{m}{3}+5=\frac{w}{9}\).
_________________
Like my post Send me a Kudos It is a Good manner.My Debrief: http://gmatclub.com/forum/howtoscore750and750imovedfrom710to189016.html



Math Expert
Joined: 02 Sep 2009
Posts: 58402

Re: Time n Work Problem
[#permalink]
Show Tags
30 Sep 2013, 02:07
honchos 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. Can you please help me to understand on what logic did you make this explanation 3 men would do the same work 5 days sooner than 9 women > \(\frac{m}{3}+5=\frac{w}{9}\).One man completes the job in \(m\) days > 3 men in m/3 days. One woman completes the job in \(w\) days > 9 women in w/9 days. We are told that m/3 is 5 less than w/9 > \(\frac{m}{3}+5=\frac{w}{9}\). Hope it's clear.
_________________



Manager
Joined: 26 Sep 2013
Posts: 184
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41

Re: Time n Work Problem
[#permalink]
Show Tags
20 Nov 2013, 11:58
Bunuel wrote: AndreG wrote: Bunuel wrote: 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.
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?



Math Expert
Joined: 02 Sep 2009
Posts: 58402

Re: Time n Work Problem
[#permalink]
Show Tags
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.
_________________



Intern
Joined: 15 Jul 2012
Posts: 32

Re: Time n Work Problem
[#permalink]
Show Tags
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



Math Expert
Joined: 02 Sep 2009
Posts: 58402

Re: Time n Work Problem
[#permalink]
Show Tags
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.
_________________



Manager
Joined: 26 May 2013
Posts: 92

Re: Time n Work Problem
[#permalink]
Show Tags
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.




Re: Time n Work Problem
[#permalink]
06 Feb 2014, 10:16



Go to page
1 2
Next
[ 35 posts ]



