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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 G 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 G 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 G is a function defined in the positive integers, such that G(k) is a positive integer for each positive integer k, what is the value of G(G(2019)) ? (1) G(G(m+n))=m+n , for every positive integers m,n. (2) G(n)=m implies G(m)=n, for every positive integers m,n. Answer: ____(D)__ _________________ 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 G is a function defined in the positive integers, such that G(k) is a positive integer for each positive integer k, what is the value of G(G(2019)) ? (1) G(G(m+n))=m+n , for every positive integers m,n. (2) G(n)=m implies G(m)=n, for every positive integers m,n. $$? = G\left( {G\left( {2019} \right)} \right)$$ $$\left( 1 \right)\,\,\,\left\{ \matrix{ \,G\left( {G\left( {m + n} \right)} \right) = m + n\,\,\,\left( {m,n \ge 1\,\,{\rm{ints}}} \right) \hfill \cr \,\,\,\,\,\,{\rm{Take}}\,\,\left( {m,n} \right) = \left( {2018,1} \right) \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,?\,\, = \,\,G\left( {G\left( {2018 + 1} \right)} \right)\,\, = \,\,2018 + 1\,\, = \,\,2019$$ $$\left( 2 \right)\,\,\,G\left( n \right) = m\,\,\,\, \Rightarrow \,\,\,\,\,G\left( m \right) = n\,\,\,\,\left( {m,n \ge 1\,\,{\rm{ints}}} \right)\,\,\,\,\,\left( * \right)\,$$ $${\rm{Take}}\,\,\left( {n,m} \right) = \left( {2019,G\left( {2019} \right)} \right)\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,? = G\left( {G\left( {2019} \right)} \right) = 2019$$ The correct answer is (D). 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 • 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 • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE 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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