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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 ## Prime factors/number properties tagged by: BTGmoderatorRO ##### This topic has 1 expert reply and 0 member replies ## Prime factors/number properties If {x} is the product of all even integers from 1 to x inclusive, what is the greatest prime factor of {22} + {20}? A) 23 B) 20 C) 11 D) 5 E) 2 OA is a What is the correct answer here how do you arrive at it? please help me out. Thanks ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Quote: If {x} is the product of all even integers from 1 to x inclusive, what is the greatest prime factor of {22} + {20}? A) 23 B) 20 C) 11 D) 5 E) 2 OA is a What is the correct answer here how do you arrive at it? please help me out. Thanks Hi Roland2rule, Let's take a look at your question. Since, {x} is the product of all even integers from 1 to x inclusive, therefore we can write {22} as, $$\left\{22\right\}=22\times20\times18\times16\times...\times2$$ Similarly {20} can be written in product form as: $$\left\{20\right\}=20\times18\times16\times...\times2$$ Now we are asked to find the greatest prime factor of {22}+{20}. For this purpose let's find the sum first. $$\left\{22\right\}+\left\{20\right\}=\left(22\times20\times18\times16\times...\times2\right)+\left(20\times18\times16\times...\times2\right)$$ Factor out (20 x 18 x 16 x .. x 2), we get $$\left\{22\right\}+\left\{20\right\}=\left(20\times18\times16\times...\times2\right)\left(22+1\right)$$ $$\left\{22\right\}+\left\{20\right\}=\left(20\times18\times16\times...\times2\right)23$$ Now we can see all the factors of {22}+{20}, Except 23 which is a prime factor, all other factors are even integers that are not prime. Therefore, the greatest prime factor of {22}+{20} is 23. 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 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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