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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42 GPA: 3.82
If the greatest common divisor of (n-1)!, n!, and (n+1)! is 5040, what  [#permalink]

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Question Stats: 48% (01:58) correct 52% (02:24) wrong based on 57 sessions

### HideShow timer Statistics [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

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Math Expert V
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Posts: 7764
Re: If the greatest common divisor of (n-1)!, n!, and (n+1)! is 5040, what  [#permalink]

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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
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Re: If the greatest common divisor of (n-1)!, n!, and (n+1)! is 5040, what  [#permalink]

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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)
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Abhishek....

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Math Revolution GMAT Instructor V
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]

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=>

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.

_________________ 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  