factorial problem

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gmat009: Master | Next Rank: 500 Posts; Posts: 458; Joined: Sun Aug 31, 2008 10:44 amFollowed by: 1 member; Thanked: 3 times

by gmat009 » Mon Nov 17, 2008 10:15 am

I am not sure if this question has been discussed before.
I tried to search it but couldn't find.

Can someone explain me what this question is really asking for.
What exactly do we need to prove.

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Source: Beat The GMAT — Data Sufficiency | Mon Nov 17, 2008 10:15 am

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Mon Nov 17, 2008 3:10 pm

Its basically asking if k is prime or not. If k were prime then 1 and k would be the only factors and there would be no p a factor of k such that
1<p<k

Stmt I

k>4!
4!=24

If k=25 the answer is yes
If k = 29 the answer is no

INSUFF

Stmt II

13!+2<=k<=13!+13

Any number between 13!+2 and 13!+13 will always be non prime i.e they will have factors from 2-13 (write out 13! = 13*12*11*10*9*8*7*6*5*4*3*2*1 )

Once a number is divisible by 2,3,4...if u keep adding 2 or 3 or 4... it will always be divisible by it again

This tell us k is non prime and 1<p<k exists

B)

Hope this helps! Let me know if u still have questions

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