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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 ## If 2 and 17 are factors of positive integer n, then which of ##### This topic has 3 expert replies and 0 member replies ### Top Member ## If 2 and 17 are factors of positive integer n, then which of ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult If 2 and 17 are factors of positive integer n, then which of the following must also divide into n? I. 34 II. 68 III. 136 A. I only B. II only C. I and II only D. I and III only E. None OA A Source: Manhattan Prep ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2791 messages Followed by: 18 members Upvotes: 43 Top Reply BTGmoderatorDC wrote: If 2 and 17 are factors of positive integer n, then which of the following must also divide into n? I. 34 II. 68 III. 136 A. I only B. II only C. I and II only D. I and III only E. None OA A Source: Manhattan Prep Since the LCM of 2 and 17 is 34, we see that, of the answer choices, only 34 must divide into n. Answer: A _________________ 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 ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15348 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 Top Reply BTGmoderatorDC wrote: If 2 and 17 are factors of positive integer n, then which of the following must also divide into n? I. 34 II. 68 III. 136 A. I only B. II only C. I and II only D. I and III only E. None 2 and 17 have no factors in common. Since n must be divisible by both 2 and 17 -- and 2*17 = 34 -- n must be a MULTIPLE OF 34. Thus, n must be divisible by I. Eliminate any answer choice that does not include I. Eliminate B and E. If n=34, then n is not divisible by II or III. Eliminate any remaining answer choice that include II or III. Eliminate C and D. The correct answer is A. _________________ 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 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 BTGmoderatorDC wrote: If 2 and 17 are factors of positive integer n, then which of the following must also divide into n? I. 34 II. 68 III. 136 A. I only B. II only C. I and II only D. I and III only E. None Source: Manhattan Prep $$n \ge 1\,\,{\mathop{\rm int}}$$ $$\left\{ \matrix{ {n \over 2} = {\mathop{\rm int}} \hfill \cr {n \over {17}} = {\mathop{\rm int}} \hfill \cr} \right.\,\,\,\,\,\,\,$$ $$?\,\,\,:\,\,\,{n \over {\,{\rm{I}}\,{\rm{,}}\,{\rm{II}}\,{\rm{,}}\,{\rm{III}}\,}}\,\,\,\mathop = \limits^? \,\,\,{\mathop{\rm int}}$$ $${\rm{I}}.\,\,\,\,{n \over {34}}\,\, = \,\,{n \over {2 \cdot 17}}\,\,\mathop = \limits^{GCF\,\left( {2,17} \right)\,\, = \,\,1} \,\,\,\,{\mathop{\rm int}} \,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,$$ $${\rm{II}}.\,\,\,\,{n \over {68}}\,\,\,\mathop = \limits^? \,\,\,{\mathop{\rm int}} \,\,\,\,,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,\,\,\,\left[ {\,{\rm{Take}}\,\,n = 34\,} \right]$$ $${\rm{III}}.\,\,\,\,{n \over {136}}\,\,\,\mathop = \limits^? \,\,\,{\mathop{\rm int}} \,\,\,\,,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,\,\,\,\left[ {\,{\rm{Take}}\,\,n = 34\,} \right]$$ $$\left( {\,\,\left\langle {{\rm{NO}}} \right\rangle = \,\,{\rm{not}}\,\,{\rm{necessarily}}\,} \right)$$ 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 • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • 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 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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