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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 ## ((x+y+1)/(x+y))((x+z+2)/(x+z))((x+w+3)/(x+w))>8? tagged by: fskilnik@GMATH ##### This topic has 1 expert reply and 0 member replies ### GMAT/MBA Expert ## ((x+y+1)/(x+y))((x+z+2)/(x+z))((x+w+3)/(x+w))>8? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult GMATH practice exercise (Quant Class 14) Answer: _____(A)__ _________________ 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) $$A = {{\left( {x + y + 1} \right)} \over {x + y}} \cdot {{\left( {x + z + 2} \right)} \over {x + z}} \cdot {{\left( {x + w + 3} \right)} \over {x + w}} = \left( {1 + {1 \over {x + y}}} \right)\left( {1 + {2 \over {x + z}}} \right)\left( {1 + {3 \over {x + w}}} \right)\,\,\,\mathop > \limits^? \,\,\,8$$ $$\left( 1 \right)\,\,\,x,y,z,w\,\, \ge 1\,\,\,\,{\rm{ints}}\,\,\,\, \Rightarrow \,\,\,\,\,2 \le x + y\,\,,\,\,x + z\,\,,\,\,x + w\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{ \,\,{1 \over {x + y}} \le {1 \over 2} \hfill \cr \,\,{1 \over {x + z}} \le {1 \over 2}\,\,\,\,\, \Rightarrow \,\,{2 \over {x + z}}\,\, \le \,\,2 \cdot {1 \over 2}\,\,\,\, \hfill \cr \,\,{1 \over {x + w}} \le {1 \over 2}\,\,\,\,\, \Rightarrow \,\,{3 \over {x + w}}\,\, \le \,\,3 \cdot {1 \over 2} \hfill \cr} \right.\,\,\,\,\,\,\left( * \right)$$ $$A\,\,\,\mathop < \limits^{\left( * \right)} \,\,\,\left( {1 + {1 \over 2}} \right)\left( {1 + 2 \cdot {1 \over 2}} \right)\left( {1 + 3 \cdot {1 \over 2}} \right) = {3 \over 2} \cdot 2 \cdot {5 \over 2} = {{15} \over 2}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.$$ $$\left( 2 \right)\,\,\,x < y < z < w\,\,\,\,::\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x;y;z;w} \right) = \left( {1;2;3;4} \right)\,\,\,\,\mathop \Rightarrow \limits^{{\rm{by}}\,\,\left( 1 \right)} \,\,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr \,{\rm{Take}}\,\,\left( {x;y;z;w} \right) = \left( {{1 \over 4};{1 \over 3};{1 \over 2};1} \right)\,\,\,\, \Rightarrow \,\,\,A = \left( {1 + {{12} \over 7}} \right)\left( {1 + {8 \over 3}} \right)\left( {1 + {{12} \over 5}} \right) > 2 \cdot 3 \cdot 3\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr} \right.$$ The correct answer is (A). 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 • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant 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 • FREE GMAT Exam Know how you'd score today for$0

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