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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 x and y are positive integers, is xy a multiple of 8? ##### This topic has 2 expert replies and 0 member replies ### Top Member ## If x and y are positive integers, is xy a multiple of 8? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult If x and y are positive integers, is xy a multiple of 8? (1) The greatest common divisor of x and y is 10 (2) The least common multiple of x and y is 100 OA C Source: GMAT Prep ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 Top Reply BTGmoderatorDC wrote: If x and y are positive integers, is xy a multiple of 8? (1) The greatest common divisor of x and y is 10 (2) The least common multiple of x and y is 100 Source: GMAT Prep $$x,y\,\,\, \ge \,\,1\,\,\,{\rm{ints}}$$ $${{xy} \over 8}\,\,\,\mathop = \limits^? \,\,\,{\mathop{\rm int}}$$ $$\left( 1 \right)\,\,GCD\left( {x,y} \right) = 10\,\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {10,10} \right)\,\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \,{\rm{Take}}\,\,\left( {x,y} \right)\,\, = \left( {10,10 \cdot 2} \right)\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.$$ $$\left( 2 \right)\,\,\,LCM\left( {x,y} \right) = 100\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {1,100} \right)\,\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \,{\rm{Take}}\,\,\left( {x,y} \right)\,\, = \left( {100,100} \right)\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.$$ $$\left( {1 + 2} \right)\,\,\,xy = GCD\left( {x,y} \right) \cdot LCM\left( {x,y} \right) = 10 \cdot 100\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle$$ This solution follows 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 22 Aug 2016 Posted: 1890 messages Followed by: 30 members Upvotes: 470 Top Reply BTGmoderatorDC wrote: If x and y are positive integers, is xy a multiple of 8? (1) The greatest common divisor of x and y is 10 (2) The least common multiple of x and y is 100 OA C Source: GMAT Prep Say least common multiple (LCM) and the greatest common divisor (GCD) of two numbers x and y are L and G. Note that for two numbers x and y, the product of x and y equals LCM and GCD. Thus, xy = 100*10 = 1000 Since 1000 is divisible by 8, xy is a multiple of 8. Both the statements together are sufficient. The correct answer: C Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: New York | Bangalore | Guangzhou | Buenos Aires | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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