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

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

by Max@Math Revolution » Tue Aug 14, 2018 4:35 pm

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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
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by Max@Math Revolution » Wed Aug 15, 2018 6:34 am
=>

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
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