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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 ## Which of the following is/are perfect numbers if "Perfe tagged by: GMATinsight ##### This topic has 2 expert replies and 0 member replies ### Top Member ## Which of the following is/are perfect numbers if "Perfe ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Which of the following is/are perfect numbers if "Perfect Number" is defined as number for which sum of all it's factors is twice the number. I) 6 II) 28 III) 36 A) I only B) II only C) III only D) I and II only D) I, II and III _________________ Bhoopendra Singh & Sushma Jha - Founder "GMATinsight" Testimonials e-mail: info@GMATinsight.com I Mobile: +91-9999687183 / +91-9891333772 To register for One-on-One FREE ONLINE DEMO Class Call/e-mail One-On-One Private tutoring fee - US$40 per hour & for FULL COURSE (38 LIVE Sessions)-US$1000 ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 GMATinsight wrote: Which of the following is/are perfect numbers? A "perfect number" is defined as an integer such that the sum of all its POSITIVE factors is twice the integer itself. I) 6 II) 28 III) 36 A) I only B) II only C) III only D) I and II only E) I, II and III $$?\,\,\,:\,\,\,{\rm{perfect}}\,\,{\rm{number}}$$ $${\rm{6}} \to {\rm{1 + 6 + 2 + 3}}\,\,\mathop {\rm{ = }}\limits^? \,\,{\rm{2}} \cdot {\rm{6}}\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,\, \Rightarrow \,\,\,\,\,{\rm{refute}}\,\,\,\left( B \right)\,\,,\,\,\left( C \right)\,\,$$ $${\text{28}} \to {\text{1 + 28 + 2 + 14 + 4 + 7}}\,\,\mathop {\text{ = }}\limits^? \,\,2 \cdot 28\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\, \Rightarrow \,\,\,\,\left( {{\text{and}}} \right)\,\,\,{\text{refute }}\left( A \right)\,\,$$ $$36 \to 1 + 36 + 2 + 18 + 3 + 12 + 4 + 9 + 6\,\,\mathop {\text{ = }}\limits^? \,\,2 \cdot 36\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \,\,\,\,\, \Rightarrow \,\,\boxed{\,\,{\text{?}}\,\,\,{\text{ = }}\,\,\,\left( D \right)\,\,}{\text{ }}$$ 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: 2444 messages Followed by: 18 members Upvotes: 43 GMATinsight wrote: Which of the following is/are perfect numbers if "Perfect Number" is defined as number for which sum of all it's factors is twice the number. I) 6 II) 28 III) 36 A) I only B) II only C) III only D) I and II only D) I, II and III The sum of the factors of 6 are 1 + 2 + 3 + 6 = 12, which is 2 x 6. So 6 is a perfect number. The sum of the factors of 28 are 1 + 2 + 4 + 7 + 14 + 28 = 56, which is 2 x 28. So 28 is a perfect number. The sum of the factors of 36 are 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 36 = 91, which is not 2 x 36. So 36 is not a perfect number. 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 • 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 • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • 1 Hour Free 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 • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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