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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Difficult Work/Rate Problem ##### This topic has 2 expert replies and 3 member replies ## Difficult Work/Rate Problem 13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 women can finish the same job in 6 days. In how many days can 1 man, 1 boy, and 1 woman working together finish the same job (assume constant rates for each men, women, and boys)? A) 42 B) 54 C) 21 D) 63 E) 24 Senior | Next Rank: 100 Posts Joined 07 Jul 2010 Posted: 81 messages Followed by: 2 members Upvotes: 12 Test Date: 9/9/10 GMAT Score: 760 Tough and ugly problem, I'd love to know a faster way. But algebraically here's how to do it: Rate + Rate = Total Constant Rate Remember that rate=job/day (time is always on the bottom) m=rate of a man b=rate of a boy w=rate of a woman So we know that 13(m)+7(b)=1/7 and 6(b) + 13(w)=1/6 Solve for m and w respectively so that we can calculate everything in terms of b. m=(1/7-7b)/13 w=(1/6-6b)/13 b=b We want to know what happens when we have one man, one woman and one boy So The combined constant rate = (1/7-7b)/13 + (1/6-6b)/13 + b Simplify (all the b's cancel out) and get (1/7 + 1/6) / 13 Find common denominators This is where you want to keep everything in fractions til the end. (1/7 + 1/6) / 13 = (1/13)*(1/7 + 1/6) =(1/13)*(6/(42) + 7/42)= (1/13)*(13/42) = 1/42 is the combined rate of one man, one boy, and one woman which verbally translates to 1 job per 42 days. Answer A Legendary Member Joined 29 Dec 2009 Posted: 1460 messages Followed by: 7 members Upvotes: 135 13 Men and 7 Boys finish work in 7 days. 20 people finish work in 7 days. 20 people work for total of 140 days. 1 people work for 7 days. 13 Women and 6 Boys finish work in 6 days. 19 people finish work in 6 days. 19 people work for total of 114 days. 1 people work for 6 days. Since the rate is same for all 3, 1 person(men or women or boy) fiinsh the job in 42 days. _________________ --Anand-- Master | Next Rank: 500 Posts Joined 02 Apr 2010 Posted: 174 messages Followed by: 1 members Upvotes: 6 13M+7B=1 job in 7 days. 6B+13W=1 job in 6 days. 13M+7B=(1/7)th job in 1 day 6B+13W=(1/6)th job in 1 day ________________________ 13M+13B+13W=(1/7+1/6)th job in 1 day -> 13(M+B+W)=(13/42)th job in 1 day -> M+B+W=(1/42)th job in 1 day Thus to complete (1/42)th job = 1 day and to complete 1 job = ? days -> 42 days is the answer Hope this work helps!!! ### GMAT/MBA Expert GMAT Instructor Joined 11 Apr 2010 Posted: 1179 messages Followed by: 88 members Upvotes: 447 One day work of 13M + 7B = 1/7 One day work of 6B + 13W = 1/6 One day work of (13M + 7B + 6B + 13W) or (13M + 13B + 13W) = 1/7 + 1/6 = 13/42 13M + 13B + 13W can finish the work in 42/13 days 1M + 1B + 1W can finish the work in (42/13)*13 = 42 days The correct answer is (A). _________________ Rahul Lakhani Quant Expert Gurome, Inc. https://www.GuroMe.com On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits 1-800-566-4043 (USA) +91-99201 32411 (India) ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15380 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 mattocks wrote: 13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 women can finish the same job in 6 days. In how many days can 1 man, 1 boy, and 1 woman working together finish the same job (assume constant rates for each men, women, and boys)? A) 42 B) 54 C) 21 D) 63 E) 24 When the job is undefined, we can plug in our own values for the job. 13 men and 7 boys can finish a job in 7 days: m = 1 unit/day and b = 1 unit/day. 13m + 7b = 13(1) + 7(1) = 20 units/day. Over 7 days, 7 * 20 = 140 total units. 6 boys and 13 women can finish the same job in 6 days: 6b = 6 units/day. Over 6 days, 6b = 6 * 6 = 36 units. 13w = 140 - 36 = 104 units. 13w = 104/6 = 52/3 units/day. w = (52/3)/13 = 4/3 units/day. So m + b + w = 1 + 1 + 4/3 = 10/3 units/day. So 140 units would take 140/(10/3) = 42 days. The correct answer is A. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. • Award-winning private GMAT tutoring Register now and save up to$200

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