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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 quadrilaterals ABCD and ADEF have the same areas, is AF&a tagged by: fskilnik@GMATH ##### This topic has 1 expert reply and 0 member replies ### GMAT/MBA Expert ## If quadrilaterals ABCD and ADEF have the same areas, is AF&a ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult GMATH practice exercise (Quant Class 15) If quadrilaterals ABCD and ADEF have the same areas, is AF > 28 ? (1) EF = 10 (2) CE = 24 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: 1434 messages Followed by: 32 members Upvotes: 59 fskilnik@GMATH wrote: GMATH practice exercise (Quant Class 15) If quadrilaterals ABCD and ADEF have the same areas, is AF > 28 ? (1) EF = 10 (2) CE = 24 $${S_{{\mathop{\rm ABCD}\nolimits} }} = {S_{{\rm{ADEF}}}} = {S_{{\rm{ADEG}}}} + {S_{{\rm{AGF}}}}\,\,\,\,\,\left( * \right)$$ $$AF\,\,\mathop > \limits^? \,\,28$$ $$\left( 1 \right)\,\,\left\{ \matrix{ \,{\rm{image}}\,\,{\rm{left}}:\,\,\left( * \right)\,\,4 \cdot 6 = 3 \cdot 6 + {{3 \cdot 4} \over 2}\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{viable}}\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr \,{\rm{image}}\,\,{\rm{right}}:\,\,\left( * \right)\,\,x \cdot 6 = 28 \cdot 6 + {{28 \cdot 4} \over 2}\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{viable}}\,\,\,\left( {x = {{28 \cdot 8} \over 6} > 0} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr} \right.$$ $$\left( 2 \right)\,\,\left\{ \matrix{ \,{\rm{image}}\,\,{\rm{left}}:\,\,\left( * \right)\,\,18 \cdot y = 6 \cdot y + {{6 \cdot 4} \over 2}\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{viable}}\,\,\,\,\left( {y = 1 > 0} \right) \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr \,{\rm{image}}\,\,{\rm{right}}:\,\,\left( * \right)\,\,18 \cdot y = 6 \cdot y + {{6 \cdot 28} \over 2}\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{viable}}\,\,\,\left( {y = 7 > 0} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr} \right.$$ $$\left( {1 + 2} \right)\,\,{\rm{Extremal}}\,\,{\rm{Scenario}}\,\,\,\left( {\left( * \right)\,\,{\rm{ignored}}} \right)\,\,:\,\,A{F_{\,{\rm{ExtScen}}}}\,\,\mathop < \limits^{{\rm{near}}} \,\,13 \cdot 2 = 26$$ $$\Rightarrow \,\,AF < \,\,A{F_{\,{\rm{ExtScen}}}} < 28\,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}.$$ The correct answer is (C). We follow the notations and rationale taught in the GMATH method. Regards, Fabio. POST-MORTEM: (1+2) It is possible to prove that AF < 16. See: Shobhit7´s argument _________________ 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 • 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 • Award-winning private GMAT tutoring Register now and save up to$200

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