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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 ## Let function # be defined as follows: tagged by: AAPL ##### This topic has 1 expert reply and 0 member replies ### Top Member ## Let function # be defined as follows: Let function f be defined as follows: $$f\left(x\right)=\frac{x!+\left(x+1\right)!}{\left(x+2\right)!}$$ What is the value of f(6)? $$A.\ \frac{1}{10}$$ $$B.\ \frac{1}{9}$$ $$C.\ \frac{1}{8}$$ $$D.\ \frac{1}{7}$$ $$E.\ \frac{1}{6}$$ The OA is D. I need help to solve this PS question. Please, can any expert assist me with it? Thanks. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Hello AAPL. It is simple. You just have to eval f on 6 and the simplify. I will show you: $$f\left(6\right)=\frac{6!+\left(6+1\right)!}{\left(6+2\right)!}=\frac{6!+7!}{8!}.$$ Now, we can write 7! and 8! as follows: $$7!=7\cdot6!\ \ \ \ \ \ and\ \ \ \ 8!=8\cdot7\cdot6!$$ Now, let's replace this on f(6). We will get $$f\left(6\right)=\frac{6!+7\cdot6!}{8\cdot7\cdot6!}=\frac{6!\cdot\left(1+7\right)}{6!\cdot\left(8\cdot7\right)}=\frac{8}{8\cdot7}=\frac{1}{7}.$$ So, the correct answer is D. I hope this help you. Regards. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. • Award-winning private GMAT tutoring Register now and save up to$200

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