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Re: Time n Work Problem
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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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It takes 6 days
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16 Jul 2018, 03:46
An alternate approach for a problem in a locked thread: Quote: 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 b. 4 c. 5 d. 6 e. 7 We can PLUG IN THE ANSWERS, which represent how many times a man's output exceeds that of a woman. When the correct answer is plugged in, 3 men will take 5 fewer days to complete the job than 9 women. B: 4 Let the rate for each woman = 1 unit per day and the rate for each man = 4 units per day. Since it takes 6 days for 3 women and 2 men to complete the job, the job = (rate for 3 women and 2 men)(6 days) = (3*1 + 2*4)(6) = 66 units. Time for 9 women to complete the job \(= \frac{work}{ratefor9women} = \frac{66}{(9*1)} = \frac{22}{3}\) ≈ 7 days. Time for 3 men to complete the job \(= \frac{work}{ratefor3men} = \frac{66}{(3*4)} = \frac{66}{12} = \frac{11}{2}\) ≈ 5 days. Doesn't work: Here, 3 men take only about 2 fewer days than 9 women. Eliminate B. For 3 men to take 5 fewer days, the rate for each man must INCREASE. Eliminate A. D: 6 Let the rate for each woman = 1 unit per day and the rate for each man = 6 units per day. Since it takes 6 days for 3 women and 2 men to complete the job, the job = (rate for 3 women and 2 men)(6 days) = (3*1 + 2*6)(6) = 90 units. Time for 9 women to complete the job \(= \frac{work}{ratefor9women} = \frac{90}{(9*1)} = \frac{90}{9} = 10\) days. Time for 3 men to complete the job \(= \frac{work}{ratefor3men} = \frac{90}{(3*6)} = \frac{90}{18} = 5\) days. Success! Here, 3 men take 5 fewer days than 9 women.
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Re: It takes 6 days for 3 women and 2 men working together to
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17 Jul 2018, 04:15
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 We can PLUG IN THE ANSWERS, which represent how many times a man's output exceeds that of a woman. When the correct answer is plugged in, 3 men will take 5 fewer days to complete the job than 9 women. B: 4 Let the rate for each woman = 1 unit per day and the rate for each man = 4 units per day. Since it takes 6 days for 3 women and 2 men to complete the job, the job = (rate for 3 women and 2 men)(6 days) = (3*1 + 2*4)(6) = 66 units. Time for 9 women to complete the job = \(\frac{work}{ratefor9women} = \frac{66}{(9*1)} = \frac{22}{3} ≈ 7\) days. Time for 3 men to complete the job = \(\frac{work}{ratefor3men} = \frac{66}{(3*4)} = \frac{66}{12} = \frac{11}{2} ≈ 5\) days. Doesn't work: Here, 3 men take only about 2 fewer days than 9 women. Eliminate B. For 3 men to take 5 fewer days, the rate for each man must INCREASE. Eliminate A. D: 6 Let the rate for each woman = 1 unit per day and the rate for each man = 6 units per day. Since it takes 6 days for 3 women and 2 men to complete the job, the job = (rate for 3 women and 2 men)(6 days) = (3*1 + 2*6)(6) = 90 units. Time for 9 women to complete the job = \(\frac{work}{ratefor9women} = \frac{90}{(9*1)} = \frac{90}{9} = 10\) days. Time for 3 men to complete the job = \(\frac{work}{ratefor3men} = \frac{90}{(3*6)} = \frac{90}{18} = 5\) days. Success! Here, 3 men take 5 fewer days than 9 women.
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Re: It takes 6 days for 3 women and 2 men working together to
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19 Jul 2018, 12:42
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?
A. 3 times B. 4 times C. 5 times D. 6 times E. 7 times We can let the number of days for 1 man to finish the work = m and that for 1 woman = w. Thus, the rate of 1 man = 1/m and the rate of 1 woman = 1/w. Since it takes 6 days for 3 women and 2 men working together to complete the work, we have: 6(3/w + 2/m) = 1 Since 3 men would do the same work 5 days sooner than 9 women, we have: 1/(3/m) + 5 = 1/(9/w) m/3 + 5 = w/9 Multiplying the above by 9, we have: 3m + 45 = w Substituting this into 6(3/w + 2/m) = 1, we have: 6(3/(3m + 45) + 2/m) = 1 6(1/(m + 15) + 2/m) = 1 Multiplying the above by m(m + 15), we have: 6m + 12(m + 15) = m(m + 15) 6m + 12m + 180 = m^2 + 15m m^2  3m  180 = 0 (m  15)(m + 12) = 0 m = 15 or m = 12 Since m can’t be negative, m = 15. So w = 3(15) + 45 = 90. We see that it takes a man 15 days to complete the work but 90 days for a woman to complete the same work. So a man’s output is 6 times the output of a woman. Answer: D
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Re: It takes 6 days for 3 women and 2 men working together to
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07 Nov 2018, 23:55
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 Please find attached the solution
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Re: It takes 6 days for 3 women and 2 men working together to
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26 Nov 2018, 10:10
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 3w+2m= 1/6 (in one day ) NEXT: 3 men would do the same work 5 days sooner than 9 women , SO let X be the job done by woman and let x5 be the work done by men HENCE: \(\frac{1}{x} \frac{1}{(x5)} = \frac{x5x}{x(x5)}\) i.e \(\frac{5}{x(x5)}\) (i know i got negative in numerator but still continued solving further ) \(\frac{5}{x(x5)}\) = \(\frac{1}{6}\) cross multiply \(x(x5)=30\) \(x\) = \(\frac{30}{x(x5)}\) now if i divide 30 by 5 i get 6. this was my solution to correct answer Bunuel, pushpitkc generis do you think my solution is correct ?



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Re: It takes 6 days for 3 women and 2 men working together to
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11 Jan 2019, 01:05
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 Hello all, I couldn't solve this question within time. But i did attempt it the following manner and got the answer right. Can someone tell me if this approach is correct/incorrect? Let the work be W. Now, based on the data provided  one man can do 1/3 of W  one woman can do 1/9 of W Here i am now assuming a number for W  let's say the work needed to be done is eating 27 pies. i.e. W=27 So one man can eat 9 pies and one woman can eat 3 pies. Because the question asks How many times does the output of a man exceed that of a woman?, I have understood this as Output of a man (9 pies) is x more than output of a woman (3 pies). so 9 = 3+x therefore, X=6. Let me know if this makes sense or I was just lucky to get the answer right (won't work all the time)



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Re: It takes 6 days for 3 women and 2 men working together to
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30 Apr 2019, 19:14
Hi Bunuel, I have no trouble setting up the two equations. However, I don’t know how to solve them quickly and efficiently since w and m are found in the denominators of the 1st equation and in the numerators of the 2nd equation. Please help! Thank you so much 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. Posted from my mobile device



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Re: It takes 6 days for 3 women and 2 men working together to
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30 Apr 2019, 20:25
Rurugu wrote: Hi Bunuel, I have no trouble setting up the two equations. However, I don’t know how to solve them quickly and efficiently since w and m are found in the denominators of the 1st equation and in the numerators of the 2nd equation. Please help! Thank you so much 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. Posted from my mobile device Rurugu You can refer to my method as well if it looks any easier to you. Link is here... https://gmatclub.com/forum/ittakes6d ... l#p2167832
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It takes 6 days for 3 women and 2 men working together to
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01 May 2019, 02:27
Solving quadratic equations, especially when they involve large numbers and need a lot of calculations to form the equation in the first place, is quite timeconsuming and the likelihood of calculation errors is also quite high. I doubt whether problems like this can be solved within the GMAT timeframe in the conventional manner. However, there is a much quicker way of solving this problem with a bit of logic and by taking a few hints from the answer choices:
Let the time taken by 3 men to do the work be 'x' days. Then, the time taken by 9 women to do the work is (x+5) days which means time taken for 3 women will be 3(x+5) days. If M and W are the speeds or rates of men and women respectively, then: M/W = 3(x+5)/x. In other words, a man is 3(x+5)/x times faster than a woman. 3(x+5)/x = 3 + 15/x. Since all the answer options are whole numbers 'x' must be a factor of 15, i.e. either 3, 5 or 15. It can't be 3 because that would make a man 8(3+5) times faster (7 is the highest option). x=15 would mean that 3 men complete the work in 15 days or 5 men complete in (3*15)/5=9 days. But we know that 3 women and 2 men complete in 6 days. Since men are faster than women so, if we substitute the 3 women by 3 men and we have 5 men working on the job it can be finished in less than 6 days. So 'x' cannot be 15 which leaves only 5 as the only possible value for 'x'. So a man is (3 + 15/5) = 3 +3 = 6 times faster than a woman.
Ans: D



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Re: It takes 6 days for 3 women and 2 men working together to
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02 May 2019, 02:23
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 given total work 5x/6=1/6 or say x=1/5 so for 3 men = 5+ 9 women 3*1/5*x = 5+9/5 3x=18 i.e 6 times IMO D



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Re: It takes 6 days for 3 women and 2 men working together to
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02 May 2019, 21:57
Archit3110
Could you please explain the assumptions underlying your answer? For example, what does 'x' stand for? I am a bit confused because first you got x=1/5 and then you got x=6. A detailed explanation would help us understand the process through which you arrived at your answer. Thanks.



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Re: It takes 6 days for 3 women and 2 men working together to
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12 Jul 2019, 19:05
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 We can let m = the number of days a man can complete the work by himself and w = the number of days a woman can complete the work by herself. Thus, 1/m = the rate of a man, and 1/w = the rate of a woman. We can create the equations 6(3 x 1/w + 2 x 1/m) = 1 and 1/(3 x 1/m) = 1/(9 x 1/w)  5 Simplifying the first equation, we have: 3/w + 2/m = 1/6 Multiplying the equation by 6wm, we have: 18m + 12w = mw Simplifying the second equation, we have: m/3 = w/9  5 Multiplying the equation by 9, we have: 3m = w  45 3m + 45 = w Substituting this in 18m + 12w = mw, we have: 18m + 12(3m + 45) = m(3m + 45) 18m + 36m + 540 = 3m^2 + 45m 3m^2  9m  540 = 0 m^2  3m  180 = 0 (m  15)(m + 12) = 0 m = 15 or m = 12 Since m can’t be negative, m = 15. Hence, w = 3(15) + 45 = 90. We see that a man’s rate is 6 times that of a woman’s rate since the number of days a man can complete the job is only 1/6 of the number of days a woman can complete the job. Answer: D
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Re: It takes 6 days for 3 women and 2 men working together to
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14 Jul 2019, 00:48
maelstroem wrote: 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 I did it in a similar manner. I assumed that 3 men can complete in 'x' days which means that 9 women can complete in (x+5) days and, working forward from there, got the same equation: x^2  x  20 = 0. What I want to point out here is that in this type of quadratic equation where factorization is possible it is quicker to factorize: x^2 x 20 = 0...> x^2  5x + 4x  20 = 0...> x(x5) + 4(x5) = 0...> (x5)(x+4) = 0. x=5



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