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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 ## A tank has two water pumps Alpha and Beta and one drain Gamm ##### This topic has 1 expert reply and 1 member reply ### Top Member ## A tank has two water pumps Alpha and Beta and one drain Gamm ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult A tank has two water pumps Alpha and Beta and one drain Gamma. Pump Alpha alone can fill the whole tank in x hours, and pump Beta alone can fill the whole tank in y hours. The drain can empty the whole tank in z hours such that z>x. When the tank was empty, pumps Alpha and Beta started pumping water in the tank and the drain Gamma simultaneously was draining water from the tank. When finally the tank is full, which of the following represents the amount of water in terms of the fraction of the tank which pump Alpha pumped into the tank? (A) yz/(x+y+z) (B) yz/(yz + xz - xy) (C) yz/(yz + xz + xy) (D) xyz/(yz + xz - xy) (E) (yz + xz - xy)/yz OA B Source: Veritas Prep ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15023 messages Followed by: 1859 members Upvotes: 13060 GMAT Score: 790 BTGmoderatorDC wrote: A tank has two water pumps Alpha and Beta and one drain Gamma. Pump Alpha alone can fill the whole tank in x hours, and pump Beta alone can fill the whole tank in y hours. The drain can empty the whole tank in z hours such that z>x. When the tank was empty, pumps Alpha and Beta started pumping water in the tank and the drain Gamma simultaneously was draining water from the tank. When finally the tank is full, which of the following represents the amount of water in terms of the fraction of the tank which pump Alpha pumped into the tank? (A) yz/(x+y+z) (B) yz/(yz + xz - xy) (C) yz/(yz + xz + xy) (D) xyz/(yz + xz - xy) (E) (yz + xz - xy)/yz Let x = 2 hours, y = 3 hours and z = 4 hours. Let the tank = 12 gallons. Since Alpha takes 2 hours to fill the 12-gallon tank, Alpha's rate = w/t = 12/2 = 6 gallons per hour. Since Beta takes 3 hours to fill the 12-gallon tank, Beta's rate = w/t = 12/3 = 4 gallons per hour. Since Gamma takes 4 hours to empty the 12-gallon tank, Gamma's rate = w/t = 12/4 = 3 gallons per hour. When all 3 pumps work together -- Alpha and Beta increasing the volume by 6 gallons per hour and 4 gallons per hour, Gamma reducing the volume by 3 gallons per hour -- the net gain per hour = 6+4-3 = 7 gallons. Since the net gain for all 3 pumps = 7 gallons per hour, and Alpha's rate alone = 6 gallons per hour, the fraction attributed to Alpha = 6/7. The correct answer must yield a value of 6/7 when x=2, y=3 and z=4. Only B works: yz/(yz + xz - xy) = (3*4)/(3*4 + 2*4 - 2*3) = 12/14 = 6/7. The correct answer is B. _________________ 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. ### Top Member Legendary Member Joined 29 Oct 2017 Posted: 732 messages Followed by: 4 members Work done by Alpha in 1 hour = 1/x Work done by Beta in 1 hour = 1/y Work done by Gamma in 1 hour = 1/z Total work done by 3 pumps in 1 hour = 1/x + 1/y + 1/z = (zy+xz-xy)/(xyz) Alpha's contribution to this work will be (1/x)/((zy+xz-xy)/(xyz))= (yz)/(zy+xz-xy). Hence, the correct answer is B • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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