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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 ## Is xy>3? tagged by: fskilnik@GMATH ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult GMATH practice exercise (Quant Class 14) Is xy > 3 ? (1) (7^x) > 729 (2) (9^y) = 7 Answer: _____(C)__ P.S.: this IS in GMAT´s quant section scope. _________________ 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) Is xy > 3 ? (1) (7^x) > 729 (2) (9^y) = 7 $$xy\,\,\mathop > \limits^? \,\,3$$ $$\left( 1 \right)\,\,{7^x} > 729\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {4,0} \right)\,\,\,\,\,\left[ {{7^4} = {{49}^2}} \right]\,\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {4,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.$$ $$\left( 2 \right)\,\,{9^y} = 7\,\,\,\, \Rightarrow \,\,\,y = {y_p}\,\,\,{\rm{unique}}\,\,{\rm{,}}\,\,\,{1 \over 2}\,\,{\rm{ < }}\,\,{y_p} < 1\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {0,{y_p}} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {6,{y_p}} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.$$ $$\left( {1 + 2} \right)\,\,\,{3^6} = 729\,\,\,\mathop < \limits^{\left( 1 \right)} \,\,\,{7^x}\,\,\mathop = \limits^{\left( 2 \right)} \,\,\,{\left( {{9^y}} \right)^x} = {3^{2xy}}\,\,\,\,\,\mathop \Rightarrow \limits^{3\,\, > \,\,1} \,\,\,2xy > 6\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle$$ The correct answer is (C). 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 ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13046 messages Followed by: 1253 members Upvotes: 5254 GMAT Score: 770 fskilnik@GMATH wrote: Is xy > 3 ? (1) (7^x) > 729 (2) (9^y) = 7 Target question: Is xy > 3 ? Statement 1: (7^x) > 729 Since there's no information about y, we cannot answer the target question with certainty. Statement 1 is NOT SUFFICIENT Statement 2: (9^y) = 7 Since there's no information about x, we cannot answer the target question with certainty. Statement 2 is NOT SUFFICIENT Statements 1 and 2 combined Statement 1 tells us that (7^x) > 729 Statement 2 tells us that (9^y) = 7 Take the inequality (7^x) > 729, and replace 7 with 9^y to get: (9^y)^x > 729 Simplify to get: 9^xy > 729 Rewrite 729 as 9^3 to get: 9^xy > 9^3 From this, we can conclude that xy > 3 Since we can answer the target question with certainty, the combined statements are SUFFICIENT Answer: C Cheers, Brent _________________ Brent Hanneson – Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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