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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 ## 190 students go to a school bake sale. 95 buy a chocolate tagged by: AAPL ##### This topic has 3 expert replies and 0 member replies ### Top Member ## 190 students go to a school bake sale. 95 buy a chocolate ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Princeton Review 190 students go to a school bake sale. 95 buy a chocolate chip cookie, 75 buy a peanut butter cookie, and at least 12 buy both. What is the least number of students who could have bought neither type of cookie? A. 10 B. 24 C. 30 D. 32 E. 45 OA D. ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10129 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi All, We're told that 190 students go to a school bake sale. Of those students, 95 buy a chocolate chip cookie, 75 buy a peanut butter cookie, and AT LEAST 12 buy both. We're asked for the LEAST number of students who could have bought NEITHER type of cookie. This question is a variation on a standard Overlapping Sets question (although there is a 'twist'; AT LEAST 12 students bought both types of cookie), but we can still use the Overlapping Sets Formula: Total = (1st group) + (2nd group) - (Both) + (Neither) Based on the given information, the equation would look like this: 190 = (95) + (75) - (AT LEAST 12) + (Neither) 190 = 170 - (AT LEAST 12) + (Neither) 20 = (Neither) - (AT LEAST 12) To minimize the "neither group", we have to make the "both" group as SMALL as possible. In this case, that would be exactly 12 people... 20 + 12 = Neither 32 = Neither Final Answer: D GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 AAPL wrote: Princeton Review 190 students go to a school bake sale. 95 buy a chocolate chip cookie, 75 buy a peanut butter cookie, and at least 12 buy both. What is the least number of students who could have bought neither type of cookie? A. 10 B. 24 C. 30 D. 32 E. 45 Excellent opportunity for the Venn diagram (aka overlapping sets)! $$? = {\left( R \right)_{\min }}$$ $$R = 190 - \left( {95 + 75 - {\rm{both}}} \right) = 20 + {\rm{both}}$$ $${\rm{both}} \ge 12\,\,\,\left( {{\rm{given}}} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,? = 32$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2424 messages Followed by: 18 members Upvotes: 43 AAPL wrote: Princeton Review 190 students go to a school bake sale. 95 buy a chocolate chip cookie, 75 buy a peanut butter cookie, and at least 12 buy both. What is the least number of students who could have bought neither type of cookie? A. 10 B. 24 C. 30 D. 32 E. 45 OA D. We can use the equation: #total = #chocolate chip + #peanut butter - #both + #neither #neither = #total - #chocolate chip - #peanut butter + #both As we can see from the equation, keeping everything else constant, the number of students who purchase neither kind of cookie decreases as the number of students who purchase both kinds decreases. Therefore, to minimize #neither, we should minimize #both: 190 = 95 + 75 - 12 + neither 190 = 158 + neither 32 = neither Answer: D _________________ 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 • 1 Hour Free 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 • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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