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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 product of integers a, b, and c if... tagged by: BTGmoderatorLU This topic has 3 expert replies and 0 member replies Top Member What is the product of integers a, b, and c if... What is the product of integers a, b, and c if $$2^a\ \cdot\ 3^b\ \cdot\ 5^c\ =\ 270,000,000$$ A. 141 B. 147 C. 162 D. 235 E. 270 The OA is B. Please, can any expert assist me with this PS question? I need help to solve it. Thanks. GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10014 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi LUANDATO, You should notice that all of the 'bases' are PRIME numbers, so this question is all about 'prime factorization.' To start, we have to prime factor 270,000,000 down into its 'pieces'... (270)(1,000)(1,000) = 270 = (3)(3)(3)(2)(5) 1,000 = (2)(2)(2)(5)(5)(5) Thus 270,000,000 = (2^7)(3^3)(5^7) The product of those three exponents is (7)(3)(7) = 147 Final Answer: B GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Quote: What is the product of integers a, b, and c if $$2^a\ \cdot\ 3^b\ \cdot\ 5^c\ =\ 270,000,000$$ A. 141 B. 147 C. 162 D. 235 E. 270 The OA is B. Please, can any expert assist me with this PS question? I need help to solve it. Thanks. Hi LUANDATO, Lets take a look at your question. $$2^a\ \cdot\ 3^b\ \cdot\ 5^c\ =\ 270,000,000$$ $$2^a.3^b.5^c=27\times10,000,000$$ $$2^a.3^b.5^c=\left(3\times3\times3\right)\times\left(2\times5\right)\times\left(2\times5\right)\times\left(2\times5\right)\times\left(2\times5\right)\times\left(2\times5\right)\times\left(2\times5\right)\times\left(2\times5\right)$$ $$2^a.3^b.5^c=3^3\times2^7\times5^7$$ $$a=3,\ b=7,\ c=7$$ $$abc=3\times7\times7$$ $$abc=147$$ Therefore, option B is correct. 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 09 Apr 2015 Posted: 1461 messages Followed by: 17 members Upvotes: 39 LUANDATO wrote: What is the product of integers a, b, and c if $$2^a\ \cdot\ 3^b\ \cdot\ 5^c\ =\ 270,000,000$$ A. 141 B. 147 C. 162 D. 235 E. 270 Letâ€™s break 270,000,000 into its prime factors. 270,000,000 = 27 x 10,000,000 = 3^3 x 10^7 = 2^7 x 3^3 x 5^7, so a x b x c = 7 x 3 x 7 = 147. Answer: B _________________ Jeffrey Miller Head of GMAT Instruction • 1 Hour Free 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 • 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 • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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