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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 What is the unit digit of the sum... tagged by: BTGmoderatorLU This topic has 3 expert replies and 0 member replies Top Member What is the unit digit of the sum... What is the unit digit of the sum 3^47 + 5^43 + 2^12? A) 8 B) 4 C) 9 D) 1 E) 3 The OA is A. Can any expert help me with this PS question please? Thanks. GMAT/MBA Expert GMAT Instructor Joined 04 Dec 2012 Posted: 2094 messages Followed by: 240 members Upvotes: 1443 The units digits of a given number raised various exponents will always form a pattern: 2^1 = 2 2^2= 4 2^3 = 8 2^4 = 16 2^5 = 32 2^6 = 64 2^7 = 128 2^8 = 256 2^9 = 512 As we can see, the pattern repeats after every 4th one. Every exponent that's a multiple of 4 will have a units digit of 6. We can extrapolate the rule: 2^(4n) ---> ends in 6 2^(4n + 1) ---> ends in 2 2^(4n + 2) ---> ends in 4 2^(4n + 3) ---> ends in 8 This will be true for every digit. For this problem, we need the patterns for 3's, 5's, and 2's: 3^1 = 3 3^2 = 9 3^3 = 7 (only worry about the UD) 3^4 = 1 3^5 = 3 3^6 = 9 Repeats every 4. pattern for 5's: 5^1 = 5 5^2 = 5 (only worry about UD) Pattern: the units digit will always be 5. 3^47 ---> 3^(44 + 3) ---> 3^(4n + 3) ---> UD of 7 5^43 ---> doesn't matter what the exponent is. UD = 5 2^12 ---> 2^(4n) ---> UD of 6 When we add 3 large numbers together and we're looking for the UD, we can ignore everything except the UD of those 3 numbers. 7 + 5 + 6 = 18, so the UD = 8. The answer is A. _________________ Ceilidh Erickson Manhattan Prep GMAT & GRE instructor EdM in Mind, Brain, and Education Harvard Graduate School of Education Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience. Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry! Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week. GMAT/MBA Expert GMAT Instructor Joined 04 Dec 2012 Posted: 2094 messages Followed by: 240 members Upvotes: 1443 _________________ Ceilidh Erickson Manhattan Prep GMAT & GRE instructor EdM in Mind, Brain, and Education Harvard Graduate School of Education Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience. Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry! Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week. GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Quote: What is the unit digit of the sum 3^47 + 5^43 + 2^12? A) 8 B) 4 C) 9 D) 1 E) 3 The OA is A. Can any expert help me with this PS question please? Thanks. Hi LUANDATO, Let's take a look at your question. We will first look at some of the exponents of 3, 5 and 2 to find out the pattern of units digit in each number. $$3^1,\ 3^2,\ 3^3,\ 3^4,\ 3^5,\ 3^6,\ ...$$ $$=3,\ 9,\ 27,\ 81,\ 243,\ 729,...$$ We can see that in the powers of 3, the unit digit repeats itself after every 4 numbers in the sequence. Let's now examine the pattern of 5 $$5^1,\ 5^2,\ 5^3,\ 5^4,\ 5^5,\ 5^6,\ ...$$ $$=5,\ 25,\ 125,\ 625,\ ...$$ Unit digit is 5 for all the exponents of 5. Let's now examine the pattern of 2 $$2^1,\ 2^2,\ 2^3,\ 2^4,\ 2^5,\ 2^6,\ ...$$ $$=2,\ 4,\ 8,\ 16,\ 32,\ 64,\ ...$$ Now using these patterns we will find out the unit digit of 3^47. Since unit digit in exponents of 3's sequence repeats after every 4 exponents. 47th power = 4(11) + 3 => 3rd exponent's unit digit in 3's sequence is 7 For all the exponents of 5 unit digit is 5, so unit digit of 5^43 is 5. Now, we will find out the unit digit of 2^12. Since unit digit in exponents of 2's sequence repeats after every 4 exponents. 12th power = 2(6)+0 => last exponent's unit digit in 2's sequence is 6 Let's now add up all the unit digits = 7 + 5 + 6 = 18 Hence, the unit digit is 8. 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. • FREE GMAT Exam Know how you'd score today for$0

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