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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 ## The graphs of f(x) = x^3-x and g(x) = mx+n are represent tagged by: fskilnik@GMATH ##### This topic has 1 expert reply and 0 member replies ### GMAT/MBA Expert ## The graphs of f(x) = x^3-x and g(x) = mx+n are represent ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult GMATH practice exercise (Quant Class 20) The graphs of f(x) = x^3-x and g(x) = mx+n are represented in the figure given. If m and n are constants, what is the value of mn ? (A) -4 (B) -2 (C) 2 (D) 4 (E) 6 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 Top Reply fskilnik@GMATH wrote: GMATH practice exercise (Quant Class 20) The graphs of f(x) = x^3-x and g(x) = mx+n are represented in the figure given. If m and n are constants, what is the value of mn ? (A) -4 (B) -2 (C) 2 (D) 4 (E) 6 $$? = m \cdot n$$ $$f\left( x \right) = {x^3} - x = x\left( {{x^2} - 1} \right) = x\left( {x + 1} \right)\left( {x - 1} \right)$$ $$f\left( 2 \right) = 6\,\,\,\,\,\, \Rightarrow \,\,\,\,\,A = \left( {2,6} \right)$$ $$f\left( x \right) = 0\,\,\,\, \Rightarrow \,\,\,\,x = - 1,0,\,{\rm{or}}\,\,1\,\,\,\,\,\, \Rightarrow \,\,\,\,\,B = \left( { - 1,0} \right)$$ $$g\left( x \right) = mx + n$$ $${\rm{line}}\,\,g\,\,:\,\,\,\left\{ \matrix{ \,m = {\rm{slope}} = {{6 - 0} \over {2 - \left( { - 1} \right)}} = 2 \hfill \cr \,B\, \in \,{\rm{graph}}\left( g \right)\,\,\,\, \Rightarrow \,\,\,\,0 = m \cdot \left( { - 1} \right) + n\,\,\,\,\, \Rightarrow \,\,\,\,\,n = 2 \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 2 \cdot 2$$ 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 • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for 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 • 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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