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

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

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22 Dec 2005, 17:32
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Does the integer k have a factor p such that 1 < p < k? OG 257

(1) k > 4!
(2) 13! + 2 <= k <= 13! + 13

I could not quite understand OG's explanation for this one. Can anyone explain this? Thanks!
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JAI HIND!

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22 Dec 2005, 17:39
JAI HIND wrote:
Does the integer k have a factor p such that 1 < p < k? OG 257

(1) k > 4!
(2) 13! + 2 <= k <= 13! + 13

I could not quite understand OG's explanation for this one. Can anyone explain this? Thanks!

Basically the stem is asking whether k is not a prime.

1) k>4! ... k>24....numbers greater than 24 can be prime or non-prime...INSUFF

2) This means k can be any of the following:

13! + 2
13! + 3
13! + 4
13! + 5
13! + 6
13! + 7
13! + 8
13! + 9
13! + 10
13! + 11
13! + 12
13! + 13

Since 13! contains the numbers 2 through 13 as factors, all of the above must have, in order from top to bottom, 2 through 13 as factors, hence they are non prime... SUFF

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22 Dec 2005, 18:32
yb wrote:
JAI HIND wrote:
Does the integer k have a factor p such that 1 < p < k? OG 257

(1) k > 4!
(2) 13! + 2 <= k <= 13! + 13

I could not quite understand OG's explanation for this one. Can anyone explain this? Thanks!

Basically the stem is asking whether k is not a prime.

1) k>4! ... k>24....numbers greater than 24 can be prime or non-prime...INSUFF

2) This means k can be any of the following:

13! + 2
13! + 3
13! + 4
13! + 5
13! + 6
13! + 7
13! + 8
13! + 9
13! + 10
13! + 11
13! + 12
13! + 13

Since 13! contains the numbers 2 through 13 as factors, all of the above must have, in order from top to bottom, 2 through 13 as factors, hence they are non prime... SUFF

agreed.

13! + 2 is a multiple of 2.
13! + 3 is a multiple of 3.
13! + 4
13! + 5
13! + 6
13! + 7
13! + 8
13! + 9
13! + 10
13! + 11
13! + 12
13! + 13 is a multiple of 13.

so anone is a prime. so B is suff..
Re: DS: Factor   [#permalink] 22 Dec 2005, 18:32
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# Does the integer k have a factor p such that 1 < p <

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