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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 ## In a village of 100 households, 75 least one DVD player, 80 tagged by: AAPL ##### This topic has 2 expert replies and 0 member replies ### Top Member ## In a village of 100 households, 75 least one DVD player, 80 ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult GMAT Prep In a village of 100 households, 75 at least have one DVD player, 80 have at least one cell phone, and 55 have at least one MP3 player. If x and y are respectively the greatest and lowest possible number of households that have all three of these devices, x-y is: A. 65 B. 55 C. 45 D. 35 E. 25 OA C ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15348 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 AAPL wrote: GMAT Prep In a village of 100 households, 75 at least have one DVD player, 80 have at least one cell phone, and 55 have at least one MP3 player. If x and y are respectively the greatest and lowest possible number of households that have all three of these devices, x-y is: A. 65 B. 55 C. 45 D. 35 E. 25 Let D = DVD owners, C = cellphone owners, and M = MP3 owners. T = D + C + M - (DC + DM + CM) - 2(DCM). The big idea with overlapping group problems is to SUBTRACT THE OVERLAPS. When we add together everyone in D, everyone in C, and everyone in M: Those in exactly 2 of the groups (DC + DM + CM) are counted twice, so they need to be subtracted from the total ONCE. Those in all 3 groups (DCM) are counted 3 times, so they need to be subtracted from the total TWICE. By subtracting the overlaps, we ensure that no one is overcounted. In the problem above: T = 100 D = 75 C = 80 M = 55. Thus: 100 = 75 + 80 + 55 - (DC + DM + CM) - 2(DCM) (DC + DM + CM) + 2(DCM) = 110. MAXIMUM: To maximize the value of DCM, we must MINIMIZE the value of DC + DM + CM. If DC + DM + CM = 0, we get: 0 + 2(DCM) = 110 DCM = 55. MINIMUM: To MINIMIZE the value of DCM, we must MAXIMIZE the value of DC + DM + CM. Since D=75, the maximum possible value of CM = 100-75 = 25. Since C=80, the maximum possible value of DM = 100-80 = 20. Since M=55, the maximum possible value of DC = 100-55 = 45. Since the maximum value of DC + DM + CM = 45+20+25 = 90, we get: 90+ 2(DCM) = 110. DCM = 10. Thus: x-y = 55-10 = 45. The correct answer is C. For similar problems, check here: http://www.beatthegmat.com/group-of-students-t263753.html http://www.beatthegmat.com/sets-t148362.html _________________ 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: 2791 messages Followed by: 18 members Upvotes: 43 AAPL wrote: GMAT Prep In a village of 100 households, 75 at least have one DVD player, 80 have at least one cell phone, and 55 have at least one MP3 player. If x and y are respectively the greatest and lowest possible number of households that have all three of these devices, x-y is: A. 65 B. 55 C. 45 D. 35 E. 25 OA C The greatest possible number of households that have all three devices is 55 when all the households that have a MP3 player also have a DVD player and a cell phone. So x = 55. Since 75 + 55 = 130 and 130 - 100 = 30, then 30 households must have both a DVD player and an MP3 player. Some of these 30 households might have a cell phone and some might not. Since 30 + 80 = 110 and 110 - 100 = 10, then 10 households must have a cell phone in addition to a DVD player and a MP3 player. In other words, a minimum of 10 households must have all three devices. So y = 10. Therefore, x - y = 55 - 10 = 45. Answer: C _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • Free Practice Test & Review How would you score if you took the GMAT 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 • 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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