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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^3 - 2x^2 + x - 1)^2 - 1=(x - a) (x - b) (x - c) (x - d tagged by: vinni.k ##### This topic has 6 expert replies and 3 member replies ### Top Member ## If (x^3 - 2x^2 + x - 1)^2 - 1=(x - a) (x - b) (x - c) (x - d If (x^3 - 2x^2 + x - 1)^2 - 1=(x - a) (x - b) (x - c) (x - d) (x - e) (x - f), then abcdef=? A. 0 B. 25 C. -25 D. 24 E. -24 OA is A How to approach this question ? Thanks ### GMAT/MBA Expert Senior | Next Rank: 100 Posts Joined 16 Dec 2014 Posted: 94 messages Followed by: 4 members Upvotes: 2 GMAT Score: 770 Top Reply vinni.k wrote: mbawisdom wrote: (x^3 - 2x^2 + x - 2) (x-2)(x^2 + 1) (x)(x-1)(x-1)((x-2)(x^2 + 1) one of a, b,c,d,e, or f = 0. therefore abcdef = 0. Answer is A. Thanks for your reply, but i have one or two doubts:- 1. How you factor out (x-2) from (x^3 - 2x^2 + x - 2) 2. (x)(x-1)(x-1)((x-2)(x^2 + 1). This gives a,b,c,d,e. "f" or any alphabet is still missing, but here x = 0. So, abcdef = 0 , even if there is no f. Please clarify. Thanks Hi, Thanks for the follow up questions (1) how did I factor out (x-2) from (x^3 - 2x^2 + x - 2) x^3 - 2x^2 + x - 2 x^2(x-2) + (x-2) (x-2)(x^2 +1) (2) so the factors are 0, 1, 1, 2, i and -i (but don't worry about the complex roots i and -i, its out of the scope of the GMAT) You are right, though, that once we have a root of zero we know abcdef =0, so we can stop at that point. ### GMAT/MBA Expert Senior | Next Rank: 100 Posts Joined 16 Dec 2014 Posted: 94 messages Followed by: 4 members Upvotes: 2 GMAT Score: 770 Top Reply vinni.k wrote: mbawisdom wrote: (x^3 - 2x^2 + x - 2) (x-2)(x^2 + 1) (x)(x-1)(x-1)((x-2)(x^2 + 1) one of a, b,c,d,e, or f = 0. therefore abcdef = 0. Answer is A. Thanks for your reply, but i have one or two doubts:- 1. How you factor out (x-2) from (x^3 - 2x^2 + x - 2) 2. (x)(x-1)(x-1)((x-2)(x^2 + 1). This gives a,b,c,d,e. "f" or any alphabet is still missing, but here x = 0. So, abcdef = 0 , even if there is no f. Please clarify. Thanks Hi, Thanks for the follow up questions (1) how did I factor out (x-2) from (x^3 - 2x^2 + x - 2) x^3 - 2x^2 + x - 2 x^2(x-2) + (x-2) (x-2)(x^2 +1) (2) so the factors are 0, 1, 1, 2, i and -i (but don't worry about the complex roots i and -i, its out of the scope of the GMAT) You are right, though, that once we have a root of zero we know abcdef =0, so we can stop at that point. ### GMAT/MBA Expert Senior | Next Rank: 100 Posts Joined 16 Dec 2014 Posted: 94 messages Followed by: 4 members Upvotes: 2 GMAT Score: 770 vinni.k wrote: If (x^3 - 2x^2 + x - 1)^2 - 1=(x - a) (x - b) (x - c) (x - d) (x - e) (x - f), then abcdef=? A. 0 B. 25 C. -25 D. 24 E. -24 OA is A How to approach this question ? Thanks Use difference of two squares to find the roots: a^2 - b^2 = (a+b)(a-b) (x^3 - 2x^2 + x - 1)^2 - 1 a = x^3 - 2x^2 + x - 1 b = 1 (x^3 - 2x^2 + x - 1)^2 - 1 (x^3 - 2x^2 + x - 1 + 1)(x^3 - 2x^2 + x - 1 - 1) (x^3 - 2x^2 + x)(x^3 - 2x^2 + x - 2) (x)(x^2 - 2x + 1)(x-2)(x^2 + 1) (x)(x-1)(x-1)((x-2)(x^2 + 1) one of a, b,c,d,e, or f = 0. therefore abcdef = 0. Answer is A. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 14925 messages Followed by: 1855 members Upvotes: 13060 GMAT Score: 790 vinni.k wrote: If (x^3 - 2x^2 + x - 1)^2 - 1=(x - a) (x - b) (x - c) (x - d) (x - e) (x - f), then abcdef=? A. 0 B. 25 C. -25 D. 24 E. -24 Let x=0. Plugging x=0 into (xÂ³ - 2xÂ² + x - 1)Â² - 1=(x - a)(x - b)(x - c)(x - d)(x - e)(x - f), we get: (0 - 1)Â² - 1 = (-a)(-b)(-c)(-d)(-e)(-f) 1 - 1 = abcdef 0 = abcdef. The correct answer is A. _________________ 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. ### Top Member Master | Next Rank: 500 Posts Joined 17 Apr 2011 Posted: 420 messages Followed by: 2 members Upvotes: 6 Test Date: 2016 Target GMAT Score: 700+ GMAT Score: 620 mbawisdom wrote: (x^3 - 2x^2 + x - 2) (x-2)(x^2 + 1) (x)(x-1)(x-1)((x-2)(x^2 + 1) one of a, b,c,d,e, or f = 0. therefore abcdef = 0. Answer is A. Thanks for your reply, but i have one or two doubts:- 1. How you factor out (x-2) from (x^3 - 2x^2 + x - 2) 2. (x)(x-1)(x-1)((x-2)(x^2 + 1). This gives a,b,c,d,e. "f" or any alphabet is still missing, but here x = 0. So, abcdef = 0 , even if there is no f. Please clarify. Thanks ### Top Member Master | Next Rank: 500 Posts Joined 17 Apr 2011 Posted: 420 messages Followed by: 2 members Upvotes: 6 Test Date: 2016 Target GMAT Score: 700+ GMAT Score: 620 GMATGuruNY wrote: Let x=0. Plugging x=0 into (xÂ³ - 2xÂ² + x - 1)Â² - 1=(x - a)(x - b)(x - c)(x - d)(x - e)(x - f), we get: (0 - 1)Â² - 1 = (-a)(-b)(-c)(-d)(-e)(-f) 1 - 1 = abcdef 0 = abcdef. The correct answer is A. Mitch, Thanks for your reply. I also tried x = 0. In fact, i tried x = 1, x = 2, and x = 3. I got the answer from x = 1, and x =2, but if i took bigger values of x , then i am not getting the answer. Is there a reason that i should stick with the smaller values of x ? Please clarify thanks ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 14925 messages Followed by: 1855 members Upvotes: 13060 GMAT Score: 790 vinni.k wrote: GMATGuruNY wrote: Let x=0. Plugging x=0 into (xÂ³ - 2xÂ² + x - 1)Â² - 1=(x - a)(x - b)(x - c)(x - d)(x - e)(x - f), we get: (0 - 1)Â² - 1 = (-a)(-b)(-c)(-d)(-e)(-f) 1 - 1 = abcdef 0 = abcdef. The correct answer is A. Mitch, Thanks for your reply. I also tried x = 0. In fact, i tried x = 1, x = 2, and x = 3. I got the answer from x = 1, and x =2, but if i took bigger values of x , then i am not getting the answer. Is there a reason that i should stick with the smaller values of x ? Please clarify thanks We are asked to determine the value of abcdef. If x=0, then x disappears from the right side of the question, leaving only the value of abcdef -- the very value that we seek to determine. For this reason, it makes sense to test x=0. As shown in my solution above: When x=0, abcdef = 0. Since only one of the answer choices can be correct, there is no need to test any other values for x. _________________ 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. ### Top Member Master | Next Rank: 500 Posts Joined 17 Apr 2011 Posted: 420 messages Followed by: 2 members Upvotes: 6 Test Date: 2016 Target GMAT Score: 700+ GMAT Score: 620 Experts, Thanks for your reply Regards Vinni ### GMAT/MBA Expert Senior | Next Rank: 100 Posts Joined 16 Dec 2014 Posted: 94 messages Followed by: 4 members Upvotes: 2 GMAT Score: 770 vinni.k wrote: Experts, Thanks for your reply Regards Vinni No problems Vinni, thanks for engaging with us - hope we could be of some help! • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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