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# If the greatest common divisor of (n-1)!, n!, and (n+1)! is 5040, what

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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If the greatest common divisor of (n-1)!, n!, and (n+1)! is 5040, what  [#permalink]

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14 Aug 2018, 17:47
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[Math Revolution GMAT math practice question]

If the greatest common divisor of (n-1)!, n!, and (n+1)! is 5040, what is the value of n?

A. 4
B. 5
C. 6
D. 7
E. 8

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 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 Aug 2009 Posts: 7764 Re: If the greatest common divisor of (n-1)!, n!, and (n+1)! is 5040, what [#permalink] ### Show Tags 14 Aug 2018, 18:10 2 1 MathRevolution wrote: [Math Revolution GMAT math practice question] If the greatest common divisor of (n-1)!, n!, and (n+1)! is 5040, what is the value of n? A. 4 B. 5 C. 6 D. 7 E. 8 Greatest common divisor of (n-2)!, n! and (n+1)! Will be (n-1)!.. So (n-1)!=5040=2*2*2*2*3*3*5*7=1*2*3*4*5*6*7=7! Thus n-1=7.....n=8 E _________________ Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4512 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: If the greatest common divisor of (n-1)!, n!, and (n+1)! is 5040, what [#permalink] ### Show Tags 15 Aug 2018, 02:06 MathRevolution wrote: [Math Revolution GMAT math practice question] If the greatest common divisor of (n-1)!, n!, and (n+1)! is 5040, what is the value of n? A. 4 B. 5 C. 6 D. 7 E. 8 $$5040 = 2^4 x 3^2 x 5^1 x 7^1$$ We also know, $$7! = 5040$$ $$GCF {(n-1)!, n!,\&\ (n+1)!) = 5040$$ Thus, the Minimum value of the group must have 7! , If, $$(n - 1)! = 7!$$ $$n = 8$$, Thus Answer must be (E) _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7597 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If the greatest common divisor of (n-1)!, n!, and (n+1)! is 5040, what [#permalink] ### Show Tags 15 Aug 2018, 07:47 => Since n! and (n+1)! are multiples of (n-1)!, (n-1)! is their gcd. It follows that n – 1 = 7 or n = 8, since 7! = 5040. Therefore, E is the answer. Answer: E _________________ 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 1 month Online Course"
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Re: If the greatest common divisor of (n-1)!, n!, and (n+1)! is 5040, what   [#permalink] 15 Aug 2018, 07:47
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# If the greatest common divisor of (n-1)!, n!, and (n+1)! is 5040, what

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