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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, and c are positive integers, what is the remainder This topic has 3 expert replies and 0 member replies Top Member If a, b, and c are positive integers, what is the remainder Timer 00:00 Your Answer A B C D E Global Stats Difficult If a, b, and c are positive integers, what is the remainder when a - b is divided by 6? (1) a = c^3 (2) b = (c - 2)^3 OA C Source: Manhattan Prep GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 BTGmoderatorDC wrote: If a, b, and c are positive integers, what is the remainder when a - b is divided by 6? (1) a = c^3 (2) b = (c - 2)^3 Source: Manhattan Prep $$a,b,c\,\, \ge 1\,\,\,{\rm{ints}}\,\,\,\,\left( * \right)$$ $$a - b = 6Q + r\,\,,\,\,\,\left\{ \matrix{ \,Q,r\,\,\,{\mathop{\rm int}} {\rm{s}} \hfill \cr \,0 \le r \le 5 \hfill \cr} \right.$$ $$? = r$$ $$\left( 1 \right)\,\,a = {c^3}\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {a,b,c} \right) = \left( {1,1,1} \right)\,\,\,\, \Rightarrow \,\,\,\,? = 0 \hfill \cr \,{\rm{Take}}\,\,\left( {a,b,c} \right) = \left( {8,1,2} \right)\,\,\,\, \Rightarrow \,\,\,\,? = 1 \hfill \cr} \right.$$ $$\left( 2 \right)\,\,b = {\left( {c - 2} \right)^3}\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {a,b,c} \right) = \left( {1,1,3} \right)\,\,\,\, \Rightarrow \,\,\,\,? = 0 \hfill \cr \,{\rm{Take}}\,\,\left( {a,b,c} \right) = \left( {2,1,3} \right)\,\,\,\, \Rightarrow \,\,\,\,? = 1 \hfill \cr} \right.$$ $$\left( {1 + 2} \right)\,\,\,a - b = {c^3} - {\left( {c - 2} \right)^3} = \ldots = \underbrace {6{c^2} - 12c + 6}_{6Q\,\,,\,\,Q = {c^2} - 2c + 1} + 2\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 2$$ 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 25 May 2010 Posted: 15359 messages Followed by: 1865 members Upvotes: 13060 GMAT Score: 790 BTGmoderatorDC wrote: If a, b, and c are positive integers, what is the remainder when a - b is divided by 6? (1) a = c^3 (2) b = (c - 2)^3 Statement 1: No information about b. INSUFFICIENT. Statement 2: No information about a. INSUFFICIENT. Statements combined: Case 1: c=3, with the result that a=3³=27 and that b=(3-2)³=1 In this case, a-b = 27-1 = 26. Dividing 26 by 6, we get: 26/6 = 4 R2 Case 2: c=4, with the result that a=4³=64 and that b=(4-2)³=8 In this case, a-b = 64-8 = 56. Dividing 56 by 6, we get: 56/6 = 9 R2 Case 3: c=5, with the result that a=5³=125 and that b=(5-2)³=27 In this case, a-b = 125-27 = 98. Dividing 98 by 6, we get: 98/6 = 16 R2 In every case, the remainder is 2. 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 22 Aug 2016 Posted: 1984 messages Followed by: 30 members Upvotes: 470 BTGmoderatorDC wrote: If a, b, and c are positive integers, what is the remainder when a - b is divided by 6? (1) a = c^3 (2) b = (c - 2)^3 OA C Source: Manhattan Prep Note that each statement alone is not sufficient, so taking both the statements together. We have to find out the remainder when a - b is divided by 6. a - b = c^3 - (c - 2)^3 = c^3 - [c^3 - 3c^2*2 + 3c*2^2 - 2^3] = c^3 - c^3 + 6c^2 - 24c + 8 = 6c^2 - 24c + 8 = (6c^2 - 24c + 6) + 2 We see that (6c^2 - 24c + 6) is divisible by 6, thus, the remainder = 2. Sufficient. The correct answer: C Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: Manhattan Review Mumbai | Hyderabad | GRE Prep Warangal | Begumpet GRE Coaching | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Trial & Practice Exam 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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