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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 a<b<0 are integers, what is the value of a^3-b^3? tagged by: fskilnik@GMATH ##### This topic has 1 expert reply and 0 member replies ### GMAT/MBA Expert ## If a<b<0 are integers, what is the value of a^3-b^3? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult GMATH practice exercise (Quant Class 16) 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: 1449 messages Followed by: 32 members Upvotes: 59 fskilnik@GMATH wrote: GMATH practice exercise (Quant Class 16) $$? = {a^3} - {b^3}$$ $$\,a < b < 0\,\,\,{\rm{ints}}\,\,\,\,\left( * \right)$$ $$\left( 1 \right)\,\,\,\left\{ \matrix{ \,\left( {a + b} \right)\left( {a - b} \right) = 65 = 1 \cdot 65 = 5 \cdot 13 \hfill \cr \,\left( * \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,a + b < a - b\,\,\, < 0\,\,\,{\rm{ints}} \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,{\rm{I}}.\,\,\left\{ \matrix{ \,a + b = - 65 \hfill \cr \,a - b = - 1 \hfill \cr} \right.\,\,\,\,\,\,\,\,{\rm{or}}\,\,\,\,\,\,{\rm{II}}.\,\,\left\{ \matrix{ \,a + b = - 13 \hfill \cr \,a - b = - 5 \hfill \cr} \right.$$ $${\rm{I}}.\,\,\left\{ \matrix{ \,a + b = - 65 \hfill \cr \,a - b = - 1 \hfill \cr} \right.\,\,\,\,\,\mathop \Rightarrow \limits^{\left( + \right)} \,\,\,\,\,\, \ldots \,\,\,\,\, \Rightarrow \,\,\,\,\left( {a,b} \right) = \left( { - 33, - 32} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = {\left( { - 33} \right)^3} - {\left( { - 32} \right)^3}$$ $${\rm{II}}.\,\,\left\{ \matrix{ \,a + b = - 13 \hfill \cr \,a - b = - 5 \hfill \cr} \right.\,\,\,\,\,\mathop \Rightarrow \limits^{\left( + \right)} \,\,\,\,\,\, \ldots \,\,\,\,\, \Rightarrow \,\,\,\,\left( {a,b} \right) = \left( { - 9, - 4} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = {\left( { - 9} \right)^3} - {\left( { - 4} \right)^3} \ne {\left( { - 33} \right)^3} - {\left( { - 32} \right)^3}$$ $$\left( 2 \right)\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {a,b} \right) = \left( { - 2, - 1} \right)\,\,\,\, \Rightarrow \,\,\,{\rm{?}}\,\,{\rm{ = }}\,\,{\left( { - 2} \right)^{\rm{3}}} - {\left( { - 1} \right)^3}\,\, \hfill \cr \,{\rm{Take}}\,\,\left( {a,b} \right) = \left( { - 3, - 1} \right)\,\,\,\, \Rightarrow \,\,\,{\rm{?}}\,\, = {\left( { - 3} \right)^{\rm{3}}} - {\left( { - 1} \right)^3}\,\, \ne \,{\left( { - 2} \right)^{\rm{3}}} - {\left( { - 1} \right)^3}\,\, \hfill \cr} \right.$$ $$\left( {1 + 2} \right)\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{II}}.\,\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}.\,\,\,\,$$ 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 • 5-Day Free Trial 5-day free, full-access trial TTP Quant 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 • 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 • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for 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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