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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 ## Pizza, hoagies and tacos ##### This topic has 3 expert replies and 2 member replies ## Pizza, hoagies and tacos Survey results: 48 like pizza 45 like hoagies 58 like tacos 28 like pizza and hoagies 37 like hoagies and tacos 40 like pizza and tacos 25 like all the three foods. A survey was conducted to determine the popularity of three foods among students. The data collected from 75 students are summarized above. What is the number of students who like none or only one of the foods ? A) 4 B) 16 c) 17 d) 20 e) 23 any method to solve this? many thanks Legendary Member Joined 03 Feb 2014 Posted: 2073 messages Followed by: 135 members Upvotes: 955 GMAT Score: 800 There are formulas for this type of overlapping sets problem, one that has three sets. Because of their usefulness, those formulas are some of the few that I bothered to memorize for the GMAT. Memorizing them is pretty easy, because the way the formulas work is pretty obvious. The best formula in this case, one in which we know how many like two items but in which we don't know how many like exactly two items, is this one. Total = A + B + C - (The Total Of Those Who Like Two) + (1 x Those Who Like All Three) + (Those Who Like None) Here's what is going on with that formula. We add the total likes. Then we subtract all the two group overlaps. Then we have to add back the all three number once, because in subtracting the two group overlaps we subtracted the all three overlap three times, thus eliminating it totally, when actually it has to be included one time. 75 = 48 + 45 + 58 - (28 + 37 + 40) + (25) + Those Who Like None 75 = 71 + Those Who Like None Those Who Like None = 75 - 71 = 4 So now we have those who like none, and we need those who like one. Pizza: 48 - 28 - 40 + 25 = 5 Hoagies: 45 - 28 - 37 + 25 = 5 Tacos: 58 - 37 - 40 + 25 = 6 4 + 5 + 5 + 6 = 20 Choose D. _________________ Marty Murray GMAT Coach m.w.murray@hotmail.com https://infinitemindprep.com/ In Person in the New York Area and Online Worldwide Last edited by Marty Murray on Sun Aug 23, 2015 12:17 pm; edited 1 time in total ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15383 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 Quote: A survey was conducted to determine the popularity of 3 food among students. The data collected from 75 students is summarized as below 48 like Pizza 45 like Hoagies 58 like tacos 28 like pizza and hoagies 37 like hoagies and tacos 40 like pizza and tacos 25 like all three food What is the number of students who like none or only one of the foods ? A. 4 B. 16 C. 17 D. 20 E. 23 Draw a VENN DIAGRAM representing the following: 75 Total 48 like pizza 45 like hoagies 58 like tacos N = ? Complete the Venn diagram by working from the INSIDE OUT. 25 like all 3 foods: 28 like pizza and hoagies 37 like hoagies and tacos 40 like pizza and tacos Subtracting from these figures the 25 who like all 3 foods, we get: Subtracting the values in the diagram from P=48, H=45, and T=58, we get: Subtracting the values in the diagram from Total = 75, we get: Thus: Only P + Only H + Only T + N = 5 + 5 + 6 + 4 = 20. The correct answer is D. _________________ 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 Legendary Member Joined 24 Jul 2015 Posted: 2486 messages Followed by: 32 members Upvotes: 19 GMAT Score: BY PICTURE 1-st explain 2-nd explain 3-rd explain www.mathrevolution.com - The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS that allow anyone to easily solve GMAT math questions. - The easy-to-use solutions. Math skills are totally irrelevant. Forget conventional ways of solving math questions. - The most effective time management for GMAT math to date allowing you to solve 37 questions with 10 minutes to spare - Hitting a score of 45 is very easy and points and 49-51 is also doable. - Unlimited Access to over 120 free video lessons at http://www.mathrevolution.com/gmat/lesson - Our advertising video at https://www.youtube.com/watch?v=R_Fki3_2vO8 ### GMAT/MBA Expert GMAT Instructor Joined 12 Sep 2012 Posted: 2635 messages Followed by: 117 members Upvotes: 625 Target GMAT Score: V51 GMAT Score: 780 Another approach: Anyone who likes exactly one food is counted ONCE. Anyone who likes exactly two foods is counted TWICE: for instance, if I like pizza and tacos, I'm counted in the pizza group AND the taco group. Since these people are counted twice, they must be subtracted ONCE, since we only want to count each person one time. Similarly, anyone who likes all three foods is counted THREE times, and must be subtracted TWICE. Anyone who doesn't like any food isn't counted at all -- they don't appear in any of our groups -- so we have to add them back in. This means that (Pizza + Hoagies + Tacos) - (people who like exactly two) - 2*(people who like all three) + (people who like none) = Total Our only problem here is that we don't have people who are counted exactly twice! The 28 people who like pizza and hoagies INCLUDE the 25 who like all three. So we have to do a little adjusting ... 28 like pizza and hoagies - 25 who like all three = 3 who like only pizza and hoagies 37 like hoagies and tacos - 25 who like all three = 12 who like only hoagies and tacos 40 like pizza and tacos - 25 who like all three = 15 who like only pizza and tacos So we have (3 + 12 + 15) who like exactly two. Now our numbers are (Pizza + Hoagies + Tacos) = 48+45+58 (like exactly two) = 3+12+15 (like all three) = 25 Total = 75 Plugging these into our equation from above, we have (48 + 45 + 58) - (3 + 12 + 15) - 2*25 + (People who like none) = 75 Which means (People who like none) = 4. So we have 4 people who like none of the foods, and 75 - 4 - (3 + 12 + 15) - 25, or 16 who like only one. Hence our answer is 4 + 16, or 20. Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now! Junior | Next Rank: 30 Posts Joined 24 Nov 2014 Posted: 22 messages Hi everyone, Here's my video explanation of the problem. Hope you enjoy! https://youtu.be/fQlnx3SGk04 Rowan _________________ Is Your GMAT Score Stuck in the 600s? 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