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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 F is a function defined in the positive integers, such th tagged by: fskilnik@GMATH ##### This topic has 1 expert reply and 0 member replies ### GMAT/MBA Expert ## If F is a function defined in the positive integers, such th ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult GMATH practice exercise (Quant Class 14) If F is a function defined in the positive integers, such that F(k) is a positive integer for each positive integer k, what is the value of F(8)? (1) F(n+1) = (n+1)*F(n), for every positive integer n. (2) F(1)*F(1) = F(1) Answer: _____(C)__ _________________ 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 14) If F is a function defined in the positive integers, such that F(k) is a positive integer for each positive integer k, what is the value of F(8)? (1) F(n+1) = (n+1)*F(n), for every positive integer n. (2) F(1)*F(1) = F(1) $$F\left( k \right) \ge 1\,\,{\mathop{\rm int}} \,\,\,\,{\rm{for}}\,\,{\rm{each}}\,\,\,k \ge 1\,\,\,\,\left( * \right)$$ $$? = F\left( 8 \right)$$ $$\left( 1 \right)\,\,F\left( {n + 1} \right) = \left( {n + 1} \right) \cdot F\left( n \right)\,\,\,{\rm{for}}\,{\rm{each}}\,\,\,n \ge 1\,\,{\mathop{\rm int}}$$ $$\left. {\matrix{ {F\left( 2 \right) = 2 \cdot F\left( 1 \right)\,\,} \hfill \cr {F\left( 3 \right) = 3 \cdot F\left( 2 \right) = 3 \cdot 2 \cdot F\left( 1 \right)} \hfill \cr {\,\,\, \vdots } \hfill \cr {? = F\left( 8 \right) = 8 \cdot 7 \cdot 6 \cdot \ldots \cdot 3 \cdot 2 \cdot F\left( 1 \right)\,\,\,} \hfill \cr } } \right\}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left\{ {\matrix{ {\,{\rm{Take}}\,\,F\left( 1 \right) = 1\,\,\,\, \Rightarrow \,\,\,? = 8!\,\,} \hfill \cr {\,{\rm{Take}}\,\,F\left( 1 \right) = 2\,\,\,\, \Rightarrow \,\,\,? = 2 \cdot 8!} \hfill \cr } } \right.$$ $$\left( 2 \right)\,\,F\left( 1 \right) \cdot F\left( 1 \right) = F\left( 1 \right)\,\,\,\,\mathop \Rightarrow \limits^{\,:\,\,F\left( 1 \right)\,\, \ne \,0\,\,\left( * \right)} \,\,\,F\left( 1 \right) = 1$$ $$\left\{ {\matrix{ {\,{\rm{Take}}\,\,F\left( n \right) = 1\,\,\,{\rm{for}}\,{\rm{each}}\,\,\,n \ge 1\,\,{\mathop{\rm int}} \,\,\,\,\, \Rightarrow \,\,\,? = 1\,\,} \hfill \cr {\,{\rm{Take}}\,\,F\left( n \right) = \left( {n + 1} \right) \cdot F\left( n \right)\,\,\,{\rm{for}}\,{\rm{each}}\,\,\,n \ge 1\,\,{\mathop{\rm int}} \,\,\,\, \Rightarrow \,\,\,? = 8!\,} \hfill \cr } } \right.$$ $$\left( {1 + 2} \right)\,\,\,\,? = 8!\,\,\,\,\, \Rightarrow \,\,\,\,\left( {\rm{C}} \right)$$ 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 • Award-winning private GMAT tutoring Register now and save up to$200

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