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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 ## For integers a, b, and c, if ab = bc ##### This topic has 3 expert replies and 0 member replies ### Top Member ## For integers a, b, and c, if ab = bc For integers a, b, and c, if ab = bc, then which of the following must also be true? A. a = c B. a^2*b=b*c^2 C. a/c = 1 D. abc > bc E. a + b + c = 0 Can some experts show me how to solve this? OA B ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 Top Reply lheiannie07 wrote: For integers a, b, and c, if ab = bc, then which of the following must also be true? A. a = c B. a^2*b=b*c^2 C. a/c = 1 D. abc > bc E. a + b + c = 0 If ab = bc, then: ab - bc = 0 b(a - c) = 0 b = 0 or a = c Now, letâ€™s analyze the answer choices. A. a = c We see that this might not be true since b can be 0. B. a^2*b = b*c^2 If b = 0, we have a^2*b = b*c^2 since both sides will be 0. If a = c, then a^2 = c^2 and certainly we will have a^2*b = c^2*b. Answer: B _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15387 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 Top Reply lheiannie07 wrote: For integers a, b, and c, if ab = bc, then which of the following must also be true? A. a = c B. a^2*b=b*c^2 C. a/c = 1 D. abc > bc E. a + b + c = 0 ab = bc ab - bc = 0 b(a-c) = 0. Implication: Either b=0 or a-c=0. Given this constraint, prove that four of the answer choices DON'T have to be true. Case 1: b=0, a=2, c=1 In this case, A, C, D and E are not true. Eliminate A, C, D and E. The correct answer is B. _________________ 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 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 lheiannie07 wrote: For integers a, b, and c, if ab = bc, then which of the following must also be true? A. a = c B. a^2*b=b*c^2 C. a/c = 1 D. abc > bc E. a + b + c = 0 Can some experts show me how to solve this? OA B Hi lheiannie07. Let's take a look at your question. First, the question is which of the options listed MUST be true. Hence, it has to be true always. If we choose a=1, b=0 and c=2, then ab=bc=0. Now (A) a=c is FALSE. (B) a^2*b=b*c^2=0 is true, but it has to be true always. (C) a/c = 1 is FALSE, because a/c=1/2. (D) abc>bc is FALSE, because abc=0=bc. (E) a+b+c=0 is FALSE, because a+b+c=1+0+2=3. Hence, the only option that was true is (B). It implies that the correct option is B. But, if we want to show that it is always true we have to do the following: let be a, b and c general integers, hence $$\text{if}\ ab=bc\ \text{then}\ \ a\cdot\left(ab\right)=a\cdot\left(bc\right)$$ $$\Leftrightarrow\ a^2b=\left(ab\right)\cdot c$$ $$\Leftrightarrow\ a^2b=\left(bc\right)\cdot c$$ $$\Leftrightarrow\ a^2b=bc^2.$$ I hope it helps you. I'm available if you'd like a follow up. Regards. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. • 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 • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE 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 • FREE GMAT Exam Know how you'd score today for$0

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