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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 ## Last Monday N female executives (N>1) received M male man tagged by: fskilnik@GMATH ##### This topic has 1 expert reply and 0 member replies ### GMAT/MBA Expert ## Last Monday N female executives (N>1) received M male man ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult GMATH practice exercise (Quant Class 18) Last Monday N female executives (N>1) received M male managers (M>1) for a business meeting. If every person shook hands exactly once with every other person in the meeting, what is the difference between the total number of shaking hands and the number of shaking hands among the female executives only? (1) M < 11 (2) M(M+2N) = 65 Answer: _____(B)__ _________________ 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 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 fskilnik@GMATH wrote: GMATH practice exercise (Quant Class 18) Last Monday N female executives (N>1) received M male managers (M>1) for a business meeting. If every person shook hands exactly once with every other person in the meeting, what is the difference between the total number of shaking hands and the number of shaking hands among the female executives only? (1) M < 11 (2) M(M+2N) = 65 $$m,n\,\, \ge \,\,2\,\,\,{\rm{ints}}\,\,\,\,\left( * \right)$$ $$? = C\left( {m + n,2} \right) - C\left( {n,2} \right) = {{\left( {m + n} \right)\left( {m + n - 1} \right)} \over 2} - {{n\left( {n - 1} \right)} \over 2}$$ $$? = \frac{{m\left( {m + n - 1} \right) + nm + n\left( {n - 1} \right) - n\left( {n - 1} \right)}}{2} = \,\,\frac{{m\left( {m + 2n - 1} \right)}}{2}\,\,\,\,\, \Leftrightarrow \,\,\,\,\boxed{\,? = \frac{{m\left( {m + 2n - 1} \right)}}{2}\,}$$ $$\left( 1 \right)\,\,m < 11\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {m,n} \right) = \left( {2,2} \right)\,\,\,\, \Rightarrow \,\,\,{\rm{?}}\,\,{\rm{ = }}\,\,{\rm{5}} \hfill \cr \,{\rm{Take}}\,\,\left( {m,n} \right) = \left( {2,3} \right)\,\,\,\, \Rightarrow \,\,\,{\rm{?}}\,\, \ne \,\,{\rm{5}}\, \hfill \cr} \right.$$ $$\left( 2 \right)\,\,m\left( {m + 2n} \right) = 65 = 5 \cdot 13\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)\,\,{\rm{and}}\,\,\left( {**} \right)} \,\,\,\,\left( {m,m + 2n} \right) = \left( {5,13} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.$$ $$\left( {**} \right)\,\,\,m > m + 2n\,\,\,\,\, \Rightarrow \,\,\,n < 0\,\,\,\,\,\,{\rm{impossible}}$$ The correct answer is (B). We follow 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 • 5-Day Free Trial 5-day free, full-access trial TTP Quant 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 • FREE GMAT Exam Know how you'd score today for$0

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