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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 ## Working alone, three persons P, Q, and R can do a certain ##### This topic has 3 expert replies and 0 member replies ### Top Member ## Working alone, three persons P, Q, and R can do a certain ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Working alone, three persons P, Q, and R can do a certain job in 10, 12, and 15 hours respectively. What is the ratio of the maximum and minimum time taken to complete the job, if at every hour, at least 1 person must work? A. 1:3 B. 1:2 C. 1:1 D. 3:1 E. 15:4 OA E Source: e-GMAT ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1532 messages Followed by: 27 members Upvotes: 470 Top Reply BTGmoderatorDC wrote: Working alone, three persons P, Q, and R can do a certain job in 10, 12, and 15 hours respectively. What is the ratio of the maximum and minimum time taken to complete the job, if at every hour, at least 1 person must work? A. 1:3 B. 1:2 C. 1:1 D. 3:1 E. 15:4 OA E Source: e-GMAT Nice question The work will be completed in maximum time if only one among P, Q and R work; since R is the slowest, it is R who would complete the work in maximum time -- 15 hours. Now the computation of minimum time is tricky. The phrase, "at least 1 person must work" means that one, two, or even three persons can work together. It is obvious that the work will be completed in minimum time if all three work together. Time taken by P, Q and R, working together = Reciprocal of (1/10 + 1/12 + 1/15) = 180/45 hours The ratio of the maximum and minimum time taken to complete the job = 15 / (180/45) = 15/4. The correct answer: E Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: Manhattan Review India | Manhattan Review Hyderabad | Begumpet GMAT Courses | Madhapur GRE Prep | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 14881 messages Followed by: 1855 members Upvotes: 13060 GMAT Score: 790 BTGmoderatorDC wrote: Working alone, three persons P, Q, and R can do a certain job in 10, 12, and 15 hours respectively. What is the ratio of the maximum and minimum time taken to complete the job, if at every hour, at least 1 person must work? A. 1:3 B. 1:2 C. 1:1 D. 3:1 E. 15:4 Let the job = the LCM of the 3 times = 60 widgets. Maximum time: The maximum time is yielded when the slowest person -- R -- works alone. Since R takes 15 hours to complete the 60-widget job, the maximum time = 15 hours. Minimum time: The minimum time is yielded when all 3 people work together. Since P takes 10 hours to complete the 60-widget job, P's rate = 60/10 = 6 widgets per hour. since Q takes 12 hours to complete the 60-widget job, Q's rate = 60/12 = 5 widgets per hour. Since R takes 15 hours to complete the 60-widget job, R's rate = 60/15 = 4 widgets per hour. Since the combined rate for P+Q+R = 6+5+4 = 15 widgets per hour, the time for P+Q+R to complete the 60-widget job = 60/15 = 4 hours. Resulting ratio: (max time) : (min time) = 15:4. The correct answer is E. _________________ 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. ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 1767 messages Followed by: 14 members Upvotes: 43 BTGmoderatorDC wrote: Working alone, three persons P, Q, and R can do a certain job in 10, 12, and 15 hours respectively. What is the ratio of the maximum and minimum time taken to complete the job, if at every hour, at least 1 person must work? A. 1:3 B. 1:2 C. 1:1 D. 3:1 E. 15:4 The maximum amount of time to complete the job is if R , the slowest worker, works alone, and it will take him 15 hours to complete it. The minimum amount of time to complete the job is if all three people work together, and it will take them 1/(1/10 + 1/12 + 1/15) = 1/(6/60 + 5/60 + 4/60) = 1/(15/60) = 60/15 = 4 hours to complete it. Therefore, the ratio is 15:4. Answer: E _________________ Scott Woodbury-Stewart Founder and CEO • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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