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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 ## m is a multiple of 13. Is mn a multiple of 195? ##### This topic has 2 expert replies and 0 member replies ### Top Member ## m is a multiple of 13. Is mn a multiple of 195? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult m is a multiple of 13. Is mn a multiple of 195? (1) n has every factor that 45 has. (2) m is divisible by 18. OA A Source: Princeton Review ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1105 messages Followed by: 29 members Upvotes: 59 BTGmoderatorDC wrote: m is a multiple of 13. Is mn a multiple of 195? (1) n has every factor that 45 has. (2) m is divisible by 18. Source: Princeton Review $$m = 13K,\,\,K\,\,{\mathop{\rm int}} \,\,\,\,\,\left( * \right)$$ $$\frac{{m \cdot n}}{{3 \cdot 5 \cdot 13}}\,\,\mathop = \limits^? \,\,\operatorname{int} \,\,\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\,\boxed{\,\,\frac{{m \cdot n}}{{3 \cdot 5}}\,\,\,\mathop = \limits^? \,\,\,\operatorname{int} \,\,}$$ $$\left( 1 \right)\,\,\,n\,\,{\rm{has}}\,\,{\rm{3}}\,\,{\rm{and}}\,\,{\rm{5}}\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle$$ $$\left( 2 \right)\,\,\,{m \over {2 \cdot {3^2}}} = {\mathop{\rm int}} \,\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {m,n} \right) = \left( {0,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr \,{\rm{Take}}\,\,\left( {m,n} \right) = \left( {2 \cdot {3^2} \cdot 13,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr} \right.$$ 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 ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1697 messages Followed by: 28 members Upvotes: 470 BTGmoderatorDC wrote: m is a multiple of 13. Is mn a multiple of 195? (1) n has every factor that 45 has. (2) m is divisible by 18. OA A Source: Princeton Review Given that m is a multiple of 13, we have m = 13k, where k is any integer. If mn a multiple of 195, mn = 195p, where p is any integer. mn = 195p => 13kn = 195p => n = 195p/13k = 15p/k. => n = 15p/k Let's take each statement one by one. (1) n has every factor that 45 has. Since 15 is a factor 45, the answer to the question is Yes. Sufficient. (2) m is divisible by 18. => m is divisible by 13*18. Thus, mn = 195p 13*18k*n = 195p n = (5/6)*(p/k) If p/k is a multiple of 6, the answer is Yes, else no. No unique answer. Insufficient. The correct answer: A Hope this helps! -Jay _________________ Manhattan Review Locations: Manhattan Review Himayatnagar | GMAT Prep Hyderabad | GRE Prep Bangalore | Chennai GRE Coaching | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. • Free Practice Test & Review How would you score if you took the GMAT 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 • Award-winning private GMAT tutoring Register now and save up to$200

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