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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 ## Find the remainder of 2^100/12 tagged by: Vincen ##### This topic has 3 expert replies and 0 member replies ### Top Member Find the remainder of 2^100/12 A. 4 B. 2 C. 8 D. 1 E. none The OA is the option A. Is there a simple way to solve this PS question? I can I solve it? I'd appreciate your help. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Quote: Find the remainder of 2^100/12 A. 4 B. 2 C. 8 D. 1 E. none The OA is the option A. Is there a simple way to solve this PS question? I can I solve it? I'd appreciate your help. Hi Vincen, Let's take a look at your question. We need to find the remainder of $$\frac{2^{100}}{12}$$ $$=\frac{2^{2\times50}}{12}$$ $$=\frac{4^{50}}{12}$$ Let's check what happens when powers of 4 is divided by 12, starting from 4^2. $$4^2=16$$ $$\frac{16}{12}=1\ remainder\ 4$$ $$4^3=64$$ $$\frac{64}{12}=5\ remainder\ 4$$ $$4^4=256$$ $$\frac{256}{12}=21\ remainder\ 4$$ $$4^5=1024$$ $$\frac{1024}{12}=85\ remainder\ 4$$ Which shows that remainder is 4 for all the positive powers of 4. Therefore, option A is correct. Hope it helps. I am available if you'd like any follow up. _________________ 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. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15380 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 Vincen wrote: Find the remainder of 2^100/12 A. 4 B. 2 C. 8 D. 1 E. none Test easy exponents and look for a pattern. 2²/12 = 4/12 = 0 R4. 2³/12 = 8/12 = 0 R8. 2⁴/12 = 16/12 = 1 R4. 2⁵/12 = 32/12 = 2 R8. 2⁶/12 = 64/12 = 5 R4. 2⁷/12 = 128/12 = 10 R8. The cases above illustrate the following: When the exponent is EVEN, the remainder is 4. When the exponent is ODD, the remainder is 8. Since 2¹⁰⁰/12 has an even exponent, the remainder will be 4. 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. ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 Vincen wrote: Find the remainder of 2^100/12 A. 4 B. 2 C. 8 D. 1 E. none Let’s find a remainder pattern: 2^1/12 = 0 remainder 2 2^2/12 = 0 remainder 4 2^3/12 = 0 remainder 8 2^4/12 = 1 remainder 4 2^5/12 = 2 remainder 8 2^6/12 = 5 remainder 4 We see that, besides 2^1/12, we have this pattern: when 2 is raised to an even power, the remainder is 4, and when 2 is raised to an odd power the remainder is 8. Thus, 2^100/12 has a reminder of 4. Answer: A • Award-winning private GMAT tutoring Register now and save up to$200

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