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# For a positive integer n, if 5^n is a factor of 25!, but 5^n+1

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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For a positive integer n, if 5^n is a factor of 25!, but 5^n+1 [#permalink]

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19 Sep 2017, 00:09
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Question Stats:

76% (00:41) correct 24% (00:20) wrong based on 76 sessions

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[GMAT math practice question]

For a positive integer n, if $$5^n$$ is a factor of 25!, but $$5^{n+1}$$ is not a factor of 25!, what is the value of n?

A. 5
B. 6
C. 7
D. 8
E. 9
[Reveal] Spoiler: OA

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"Only $79 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Sep 2009 Posts: 44421 Re: For a positive integer n, if 5^n is a factor of 25!, but 5^n+1 [#permalink] ### Show Tags 19 Sep 2017, 00:26 MathRevolution wrote: [GMAT math practice question] For a positive integer n, if $$5^n$$ is a factor of 25!, but $$5^{n+1}$$ is not a factor of 25!, what is the value of n? A. 5 B. 6 C. 7 D. 8 E. 9 Similar question also posted by you: https://gmatclub.com/forum/for-a-positi ... 27957.html _________________ Director Status: Preparing for GMAT Joined: 25 Nov 2015 Posts: 526 Location: India GPA: 3.64 Re: For a positive integer n, if 5^n is a factor of 25!, but 5^n+1 [#permalink] ### Show Tags 19 Sep 2017, 03:15 MathRevolution wrote: [GMAT math practice question] For a positive integer n, if $$5^n$$ is a factor of 25!, but $$5^{n+1}$$ is not a factor of 25!, what is the value of n? A. 5 B. 6 C. 7 D. 8 E. 9 25! has five 5s. because 25/5 = 5 hence 5^5 will completely divide 25! but not 5^6 Answer 6 (B) _________________ Please give kudos, if you like my post When the going gets tough, the tough gets going... Manager Joined: 17 Aug 2016 Posts: 51 Re: For a positive integer n, if 5^n is a factor of 25!, but 5^n+1 [#permalink] ### Show Tags 19 Sep 2017, 12:36 MathRevolution wrote: [GMAT math practice question] For a positive integer n, if $$5^n$$ is a factor of 25!, but $$5^{n+1}$$ is not a factor of 25!, what is the value of n? A. 5 B. 6 C. 7 D. 8 E. 9 This question basically asks us to find the find what could be the maximum value of n OR one can say that what is the highest multiple of 5 which can divide 25! completely. There are two ways to find the number of 5s in 25! to solve this - 1. Check factors of 5s in 25! : 5,10,15,20,25 The total number of 5s (n) are = 1 + 1+ 1 + 1 + 2 = 6 Thus n = 6, because n +1 = 7 and $$5^n+1$$ would not be a factor of 25!. 2. Division method of finding the number of 5s. 25/5 = 5 5/5 = 1 Thus total 5s are = 5 + 1 = 6. The correct answer is Option B. _________________ Work Hard! Have Fun! Create History! Manager Joined: 17 Aug 2016 Posts: 51 Re: For a positive integer n, if 5^n is a factor of 25!, but 5^n+1 [#permalink] ### Show Tags 19 Sep 2017, 12:42 souvonik2k wrote: MathRevolution wrote: [GMAT math practice question] For a positive integer n, if $$5^n$$ is a factor of 25!, but $$5^{n+1}$$ is not a factor of 25!, what is the value of n? A. 5 B. 6 C. 7 D. 8 E. 9 25! has five 5s. because 25/5 = 5 hence 5^5 will completely divide 25! but not 5^6 Answer 6 (B) A slight mistake I guess. 25/5 = 5, but then 5/5 = 1 also needs to be done. So total 5s in 25! would be 6. Had the number be say 15! or 18! then we could have done a single division and that would have been suffice to get the number of 5s. Regards, Squib _________________ Work Hard! Have Fun! Create History! Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5079 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: For a positive integer n, if 5^n is a factor of 25!, but 5^n+1 [#permalink] ### Show Tags 21 Sep 2017, 00:58 => 25! = 1 x 2 x … x 5 x … x 10 x … x 15 x … x 20 x … x 25 = 1 x … x 4 x 6 x … x 9 x 11 x … x 14 x 16 x … x 19 x 21 x … x 24 x 5 x 10 x 15 x 20 x 25 = 1 x … x 4 x 6 x … x 9 x 11 x … x 14 x 16 x … x 19 x 21 x … x 24 x ( 5 x 5 x 2 x 5 x 3 x 5 x 4 x 5^2 ) = 1 x … x 4 x 6 x … x 9 x 11 x … x 14 x 16 x … x 19 x 21 x … x 24 x (2 x 3 x 4 x 5^6 ) Thus n = 6. Ans: B _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 3 month Online Course"
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Re: For a positive integer n, if 5^n is a factor of 25!, but 5^n+1   [#permalink] 21 Sep 2017, 00:58
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