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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 ## At a family summer party, each of the x members of the tagged by: swerve ##### This topic has 3 expert replies and 0 member replies ### Top Member ## At a family summer party, each of the x members of the ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult At a family summer party, each of the x members of the family chose whether or not to have a hamburger and whether or not to have a hotdog. If 1/3 chose to have a hamburger, and of those 1/7 chose to also have a hotdog, then how many family members chose NOT to have both? A. x/21 B. x/10 C. 9x/10 D. 10x/21 E. 20x/21 The OA is E. Source: EMPOWERgmat ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15348 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 swerve wrote: At a family summer party, each of the x members of the family chose whether or not to have a hamburger and whether or not to have a hotdog. If 1/3 chose to have a hamburger, and of those 1/7 chose to also have a hotdog, then how many family members chose NOT to have both? A. x/21 B. x/10 C. 9x/10 D. 10x/21 E. 20x/21 Let the x family members = the product of the two denominators = 3*7 = 21. Number who chose to have a hamburger = (1/3)(21) = 7. Since 1/7 of the hamburger-eaters also had a hot dog, the number who had both = (1/7)(7) = 1. Thus, the number who did NOT have both = (total members) - (number who had both) = 21-1 = 20. The correct answer must yield a value of 20 when x=21. Only E works: (20/21)x = (20/21)(21) = 20. 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 08 Dec 2008 Posted: 12982 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 swerve wrote: At a family summer party, each of the x members of the family chose whether or not to have a hamburger and whether or not to have a hotdog. If 1/3 chose to have a hamburger, and of those 1/7 chose to also have a hotdog, then how many family members chose NOT to have both? A. x/21 B. x/10 C. 9x/10 D. 10x/21 E. 20x/21 The OA is E. Source: EMPOWERgmat Let's use the INPUT-OUTPUT approach. It might be useful to choose a number that works well with the fractions given in the question (1/3 and 1/7). So, let's say there are 21 family members at the party. In other words, we're saying that x = 21 1/3 chose to have a hamburger, and of those 1/7 chose to also have a hotdog. 1/3 of 21 is 7, so 7 people chose to have a hamburger. 1/7 of 7 = 1, so 1 person had BOTH a hamburger AND a hotdog. How many family members chose NOT to have both? If 1 person had BOTH a hamburger AND a hotdog, then the remaining 20 people did not have BOTH a hamburger AND a hotdog. So, when we INPUT x = 21, the answer to the question is "20 people did not have BOTH a hamburger AND a hotdog" Now we'll INPUT x = 21 into each answer choice and see which one yields the correct OUTPUT of 20 A. 21/21 = 1. We want an output of 20. ELIMINATE A. B. 21/10 = 2.1. We want an output of 20. ELIMINATE B. C. (9)(21)/10 = 18.9. We want an output of 20. ELIMINATE C. D. (10)(21)/21 = 10. We want an output of 20. ELIMINATE D. E. (20)(21)/21 = = 20. PERFECT! Answer: E Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2791 messages Followed by: 18 members Upvotes: 43 swerve wrote: At a family summer party, each of the x members of the family chose whether or not to have a hamburger and whether or not to have a hotdog. If 1/3 chose to have a hamburger, and of those 1/7 chose to also have a hotdog, then how many family members chose NOT to have both? A. x/21 B. x/10 C. 9x/10 D. 10x/21 E. 20x/21 Since x * 1/3 * 1/7 = x/21 of the family members have both a hamburger and a hotdog, 20x/21 of the family members do not have both. Answer: E _________________ 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 Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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