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# If x and n are positive integers, is n! + x divisible by x ?

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If x and n are positive integers, is n! + x divisible by x ? [#permalink]  08 Oct 2004, 15:45
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If x and n are positive integers, is n! + x divisible by x?

1) n > x
2) n is not a prime number

-Irene
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Joined: 16 Jun 2004
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I am getting A.

1. I am unsure if my method is a efficient one. I put some numbers for n and x with n>x. ex. 3! +2 is divisble by 2. 5! +3 is divisible by 3. However 5!+7 is not divisible by 7 (when n<x). So concluded A.

2. As illustrated above if n<x and even if n! is not a prime number - it is not divisible by x. However if n>x, it is divisible by x. Since there are two possibilities, it is Insuff.
Manager
Joined: 07 Sep 2004
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for the first one

if n>x then x is a factor of n! (1*2*3*.....*x*......*n)

this means that n!+x is a multiple of x . and is therefore divisible by x.

for the 2nd one insufficient

GMAT Club Legend
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also got A here
As long as we know x is part of n!, then it is divisible by x because you can factor out x. Hence, by knowing that n is larger than x, x can be factored out and the expression is divisible by x
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Best Regards,

Paul

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You guys are great!!! A is the OA!!
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