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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 If A = 10! + 12! + 14! + 16! +..........+100!... tagged by: BTGmoderatorLU This topic has 1 expert reply and 0 member replies Top Member If A = 10! + 12! + 14! + 16! +..........+100!... If A = 10! + 12! + 14! + 16! +..........+100!, then the highest power of 2 in A is A. 7 B. 8 C. 9 D. 10 E. 11 The OA is B. I don't understand this PS question. Can any expert explain it for me, please? Thanks. GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 LUANDATO wrote: If A = 10! + 12! + 14! + 16! +..........+100!, then the highest power of 2 in A is A. 7 B. 8 C. 9 D. 10 E. 11 The OA is B. I don't understand this PS question. Can any expert explain it for me, please? Thanks. This question isn't terribly well-worded, but the gist seems to ask, if 2^n is a factor of the sum, what is the greatest possible value of n? First, we know that every term in the series contains 10! for example: 12! = 12*11*10!, and 14! = 14*13*12*11*10!, etc. So we can re-write the sum as 10!(1 + 12*11 + 14*13*12*11 ... + 100*99*98...) Notice that inside the parentheses, every number will be even, aside from '1.' So we know that this enormous sum will be ODD, as EVEN + 1 = ODD.) Now all we have to do is count the 2's in the prime factorization of 10! 10/2 = 5 terms with at least one 2. 10/(2^2) = 10/4 = 2.5 -->2 terms with at least two 2's. 10/(2^3) = 10/8 = 1.25 --> 1 term with at least three 2's. 5 + 2 + 1 = 8. The answer is B _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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