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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 ## What is the value of a^3+b^3 ? tagged by: fskilnik@GMATH ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## 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 14) 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 25 May 2010 Posted: 15348 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 fskilnik@GMATH wrote: GMATH practice exercise (Quant Class 14) Answer: ____ (C)__ Statement 1: Case 1: a=0 and b=1, with the result that a+b = 0+1 = 1 In this case, aÂ³+bÂ³ = 0Â³ + 1Â³ = 1 Case 2: a=2 and b=-1, with the result that a+b = 2-1 = 1 In this case, aÂ³+bÂ³ = 2Â³ + (-1)Â³ = 7 Since aÂ³+bÂ³ can be different values, INSUFFICIENT. Statement 2: Case 3: a=1 and b=1, with the result that aÂ²+bÂ² = 1Â²+1Â² = 2 In this case, aÂ³+bÂ³ = 1Â³ + 1Â³ = 2 Case 4: a=-1 and b=-1, with the result that aÂ²+bÂ² = (-1)Â²+(-1)Â² = 2 In this case, aÂ³+bÂ³ = (-1)Â³ + (-1)Â³ = -2 Since aÂ³+bÂ³ can be different values, INSUFFICIENT. Statements combined: Squaring a+b = 1, we get: aÂ² + bÂ² + 2ab = 1 Substituting aÂ²+bÂ²=2 into the red equation above, we get: 2 + 2ab = 1 2ab = -1 ab = -0.5 Multiplying aÂ²+bÂ²=2 by a+b=1, we get: (aÂ²+bÂ²)(a+b) = 2*1 aÂ³ + bÂ³ + aÂ²b + abÂ² = 2 aÂ³ + bÂ³ + ab(a+b) = 2 Substituting ab=-0.5 and a+b=1 into the blue equation above, we get: aÂ³ + bÂ³ + (-0.5)(1) = 2 aÂ³ + bÂ³ = 2.5 SUFFICIENT. The correct answer is C. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### 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) $$? = {a^3} + {b^3}$$ $$\left( 1 \right)\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {a,b} \right) = \left( {1,0} \right)\,\,\,\, \Rightarrow \,\,\,? = 1 \hfill \cr \,{\rm{Take}}\,\left( {a,b} \right) = \left( {2, - 1} \right)\,\,\,\, \Rightarrow \,\,\,? \ne 1 \hfill \cr} \right.$$ $$\left( 2 \right)\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {a,b} \right) = \left( {1,1} \right)\,\,\,\, \Rightarrow \,\,\,? = 2 \hfill \cr \,{\rm{Take}}\,\left( {a,b} \right) = \left( {\sqrt 2 ,0} \right)\,\,\,\, \Rightarrow \,\,\,? \ne 2 \hfill \cr} \right.$$ $$\left( {1 + 2} \right)\,\,\,2 = \left( {a + b} \right)\left( {{a^2} + {b^2}} \right) = \underbrace {{a^3} + {b^3}}_{{\rm{focus}}} + ab\underbrace {\left( {a + b} \right)}_{ = \,1}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{?_{{\rm{temporary}}}} = ab$$ $$\left\{ \matrix{ \,{1^2} = {\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2} \hfill \cr \,2 = {a^2} + {b^2} \hfill \cr} \right.\,\,\,\,\,\mathop \Rightarrow \limits^{\left( - \right)} \,\,\,2ab = - 1\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{?_{{\rm{temporary}}}}\,\,{\rm{unique}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.$$ 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 • 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 • 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 Trial & Practice Exam BEAT THE GMAT EXCLUSIVE 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 GMAT Exam Know how you'd score today for$0

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