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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 ## Challenge question: What is the sum of all tagged by: Brent@GMATPrepNow ##### This topic has 3 expert replies and 0 member replies ### GMAT/MBA Expert ## Challenge question: What is the sum of all ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult What is the sum of all solutions to the equation x^(2/3) - x^(1/3) - 2 = 4? A) -35 B) -19 C) 7 D) 19 E) 35 Answer: D Source: www.gmatprepnow.com Difficulty level: 600 - 650 _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15257 messages Followed by: 1861 members Upvotes: 13060 GMAT Score: 790 Brent@GMATPrepNow wrote: What is the sum of all solutions to the equation x^(2/3) - x^(1/3) - 2 = 4? A) -35 B) -19 C) 7 D) 19 E) 35 x^(2/3) - x^(1/3) - 2 = 4 x^(2/3) - x^(1/3) - 6 = 0 [x^(1/3) - 3] [x^(1/3) + 2] = 0 Solution 1: x^(1/3) - 3 = 0 x^(1/3) = 3 x^(1/3)Â³ = 3Â³ x = 27 Solution 2: x^(1/3) + 2 = 0 x^(1/3) = -2 x^(1/3)Â³ = (-2)Â³ x = -8 Sum of the solutions = -8 + 27 = 19. The correct answer is D. _________________ 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 Brent@GMATPrepNow wrote: What is the sum of all solutions to the equation x^(2/3) - x^(1/3) - 2 = 4? A) -35 B) -19 C) 7 D) 19 E) 35 Source: www.gmatprepnow.com $$?\,\,\,:\,\,\,\,\,{\text{sum}}\,\,{\text{of}}\,\,{\text{roots}}\,\,{\text{of}}\,\,\,\,\root 3 \of {{x^2}} - \root 3 \of x - 6 = 0$$ $$y = \root 3 \of x \,\,\,\,\,\,\,\,\,\left[ {\,\root 3 \of {{x^2}} = {{\left( {\root 3 \of x } \right)}^2} = {y^2}\,} \right]\,$$ $${y^2} - y - 6 = 0\,\,\,\,\,\,\,\mathop \Rightarrow \limits_{{\rm{product}}\, = \, - 6}^{{\rm{sum}}\, = \,1} \,\,\,\,\,\,\,\,\left\{ \matrix{ \,3 = {y_1} = \root 3 \of {{x_1}} \,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{cubing}}} \,\,\,\,\,{x_1} = {3^3} = 27 \hfill \cr \, - 2 = {y_2} = \root 3 \of {{x_2}} \,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{cubing}}} \,\,\,\,\,{x_2} = {\left( { - 2} \right)^3} = - 8 \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,?\,\, = \,\,27 + \left( { - 8} \right)\,\, = \,\,19$$ 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 08 Dec 2008 Posted: 12832 messages Followed by: 1247 members Upvotes: 5254 GMAT Score: 770 Brent@GMATPrepNow wrote: What is the sum of all solutions to the equation x^(2/3) - x^(1/3) - 2 = 4? A) -35 B) -19 C) 7 D) 19 E) 35 Answer: D Source: www.gmatprepnow.com Difficulty level: 600 - 650 Approach #1 If we recognize that x^(2/3) = [x^(1/3)]^2, then we can use a technique called u-substitution. Let u = x^(1/3) Now take original equation and replace x^(1/3) with u to get: uÂ² - u - 2 = 4 Subtract 4 from both sides to get: to get: uÂ² - u - 6 = 0 Factor: (u - 3)(u + 2) = 0 So, the two solutions here are u = 3 and u = -2 At this point, we replace u with x^(1/3) to get: x^(1/3) = 3 and x^(1/3) = -2 If x^(1/3) = 3, then x = 27 If x^(1/3) = -2, then x = -8 So, the SUM of the solutions = 27 + -8 = 19 Answer: D --------------------------------------------------------- Approach #2 If we recognize that x^(2/3) = [x^(1/3)]^2, then we can go straight to factoring. GIVEN: x^(2/3) - x^(1/3) - 2 = 4[/m] Subtract 4 from both sides to get:x^(2/3) - x^(1/3) - 6 = 0[/m] Factor: (x^(1/3) - 3)(x^(1/3) + 2) = 0[/m] So, EITHER x^(1/3) = 3 OR x^(1/3) = -2 If x^(1/3) = 3, then x = 27 If x^(1/3) = -2, then x = -8 So, the SUM of the solutions = 27 + -8 = 19 Answer: D Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! • 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 • 5 Day FREE Trial Study Smarter, Not Harder 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 • Award-winning private GMAT tutoring Register now and save up to$200

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