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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 ## The value of 12! is closest... tagged by: BTGmoderatorLU ##### This topic has 2 expert replies and 0 member replies ### Top Member ## The value of 12! is closest... The value of 12! is closest to: A. (10^6) B. 3(10^7) C. 5(10^8) D. 7(10^9) E. 9(10^11) The OA is C. How can I determine this? Can eny expert help me with this PS question please? Thanks. ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10197 messages Followed by: 497 members Upvotes: 2867 GMAT Score: 800 Hi LUANDATO, The prompt does NOT ask us for an EXACT calculation, so we can use a bit of estimation to determine which of the answers is relatively close to 12!. It's also worth noting that these answers are NOT 'close together' - each answer is at least 10 times GREATER than the answer that precedes it, so we have to be careful about noting all of the 'powers of 10' that we're dealing with. To start, 12! = (12)(11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1) Let's starting 'grouping' together numbers that form a product that is 'close' to a multiple of 10: (12)(8) = 96 .... about 100 = 10^2 (11)(9) = 99 .... about 100 = 10^2 10 = 10 .... = 10^1 (7)(5)(3) = 105 .... about 100 = 10^2 (6)(4)(2)(1) = 48 ... about 50 = 5(10) Thus, the product is approximately: (10^2)(10^2)(10^1)(10^2)(5)(10) = 5(10^8) Final Answer: C 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: The value of 12! is closest to: A. (10^6) B. 3(10^7) C. 5(10^8) D. 7(10^9) E. 9(10^11) The OA is C. How can I determine this? Can eny expert help me with this PS question please? Thanks. Hi LUANDATO, Let's take a look at your question. We are asked to estimate the value of 12!. $$12!\ =\ 12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1$$ Let's now make groups of products that are aproximately equal to 10 or 100, $$=\ \left(12\times8\right)\times\left(11\times9\right)\times\left(10\times1\right)\times\left(7\times6\times2\right)\times\left(4\times3\right)\times5$$ $$=\ \left(96\right)\times\left(99\right)\times\left(10\right)\times\left(84\right)\times\left(12\right)\times5$$ $$\approx\left(100\right)\times\left(100\right)\times\left(10\right)\times\left(100\right)\times\left(10\right)\times5$$ $$\approx\left(10^2\right)\times\left(10^2\right)\times\left(10^1\right)\times\left(10^2\right)\times\left(10^1\right)\times5$$ $$\approx\left(10^{2+2+1+2+1}\right)\times5$$ $$\approx\left(10^8\right)\times5$$ $$\approx5\left(10^8\right)$$ Therefore, Option D is correct. Hope this 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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