It is currently 18 Oct 2017, 06:20

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
Intern
Joined: 04 Oct 2004
Posts: 12

Kudos [?]: [0], given: 0

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

### Show Tags

08 Oct 2004, 16:45
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 1 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

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

-Irene

Kudos [?]: [0], given: 0

Director
Joined: 16 Jun 2004
Posts: 891

Kudos [?]: 65 [0], given: 0

### Show Tags

08 Oct 2004, 17:03
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.

Kudos [?]: 65 [0], given: 0

Manager
Joined: 07 Sep 2004
Posts: 60

Kudos [?]: 1 [0], given: 0

### Show Tags

08 Oct 2004, 17:50
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

Kudos [?]: 1 [0], given: 0

GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4285

Kudos [?]: 527 [0], given: 0

### Show Tags

08 Oct 2004, 22:01
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
_________________

Best Regards,

Paul

Kudos [?]: 527 [0], given: 0

Intern
Joined: 04 Oct 2004
Posts: 12

Kudos [?]: [0], given: 0

### Show Tags

09 Oct 2004, 08:19
You guys are great!!! A is the OA!!

Kudos [?]: [0], given: 0

09 Oct 2004, 08:19
Display posts from previous: Sort by