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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: AAPL ##### This topic has 2 expert replies and 1 member reply ### 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 EMPOWERgmat 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 OA E. ### Top Member Junior | Next Rank: 30 Posts Joined 03 Oct 2018 Posted: 10 messages The only important thing to understand in this problem is that the group of people who choose NOT to have BOTH will include those people who have :- either one of a hotdog or hamburger who have neither Thus , we have the number of people who have both as x*(1/3)*(1/7)=x/21 Anyone not in this category chose to NOT HAVE BOTH. Therefore, x-(x/21)= 20x/21 ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12237 messages Followed by: 1239 members Upvotes: 5254 GMAT Score: 770 AAPL wrote: EMPOWERgmat 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 OA E. These kinds of questions (Variables in the Answer Choices - VIACs) can be answered algebraically or using the INPUT-OUTPUT approach. The Ash Mo solved the question algebraically, so 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 our video course along with Sign up for our free Question of the Day emails And check out all of our 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: 1643 messages Followed by: 14 members Upvotes: 43 AAPL wrote: EMPOWERgmat 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 • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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