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# Does the integer k have a factor p such that 1 < p <

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Manager
Joined: 21 Mar 2007
Posts: 75
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Does the integer k have a factor p such that 1 < p < [#permalink]  26 Mar 2008, 00:09
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Does the integer k have a factor p such that 1 < p < k?

(1) k > 4!
(2) 13! + 2 <=(less than or equal to) k <= 13! + 13

Please explain the steps you take!
Manager
Joined: 20 Aug 2007
Posts: 65
Followers: 1

Kudos [?]: 9 [0], given: 0

Re: OG DS 153 [#permalink]  26 Mar 2008, 00:38
japped187 wrote:
Does the integer k have a factor p such that 1 < p < k?

(1) k > 4!
(2) 13! + 2 <=(less than or equal to) k <= 13! + 13

Please explain the steps you take!

I'd say B
The question ask whether K is prime number or not

1) is not sufficient. k>24 says nothing. i.e. if k=31 then answer is "no" but if k=25 then answer is "yes"

2) integers from 13!+2 to 13!+13, inclusive, are all non-prime numbers.
To illustrate
13!+2 = 1*2*3*...*13 +2 ->> this is divisible by 2
13!+3 = 1*2*3*...*13 +3 ->> this is divisible by 3
13!+13 = 1*2*2*...*13 +13 ->> this is divisible by 13
Thus, 2) only is sufficient
Manager
Joined: 21 Mar 2007
Posts: 75
Followers: 1

Kudos [?]: 24 [0], given: 0

Re: OG DS 153 [#permalink]  26 Mar 2008, 02:47
prov wrote:
japped187 wrote:
Does the integer k have a factor p such that 1 < p < k?

(1) k > 4!
(2) 13! + 2 <=(less than or equal to) k <= 13! + 13

Please explain the steps you take!

I'd say B
The question ask whether K is prime number or not

1) is not sufficient. k>24 says nothing. i.e. if k=31 then answer is "no" but if k=25 then answer is "yes"

2) integers from 13!+2 to 13!+13, inclusive, are all non-prime numbers.
To illustrate
13!+2 = 1*2*3*...*13 +2 ->> this is divisible by 2
13!+3 = 1*2*3*...*13 +3 ->> this is divisible by 3
13!+13 = 1*2*2*...*13 +13 ->> this is divisible by 13
Thus, 2) only is sufficient

How did you determine that K is prime?
Manager
Joined: 20 Aug 2007
Posts: 65
Followers: 1

Kudos [?]: 9 [0], given: 0

Re: OG DS 153 [#permalink]  26 Mar 2008, 03:50
japped187 wrote:
prov wrote:
japped187 wrote:
Does the integer k have a factor p such that 1 < p < k?

(1) k > 4!
(2) 13! + 2 <=(less than or equal to) k <= 13! + 13

Please explain the steps you take!

I'd say B
The question ask whether K is prime number or not

1) is not sufficient. k>24 says nothing. i.e. if k=31 then answer is "no" but if k=25 then answer is "yes"

2) integers from 13!+2 to 13!+13, inclusive, are all non-prime numbers.
To illustrate
13!+2 = 1*2*3*...*13 +2 ->> this is divisible by 2
13!+3 = 1*2*3*...*13 +3 ->> this is divisible by 3
13!+13 = 1*2*2*...*13 +13 ->> this is divisible by 13
Thus, 2) only is sufficient

How did you determine that K is prime?

Definition of prime number is that, there are 2 factors which are 1 and that number itself.
In this question, if k has any factors that are between 1 and k, then k is not prime number. If not, then only factors shall be 1 and k.
Re: OG DS 153   [#permalink] 26 Mar 2008, 03:50
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# Does the integer k have a factor p such that 1 < p <

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