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

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

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New post 12 Nov 2017, 09:28
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Re: Does the integer k have a factor p such that 1 < p < k ?  [#permalink]

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New post 19 Dec 2017, 07:46
gmatcracker2010 wrote:
Does the integer k have a factor p such that 1<p<k?


(1) k > 4!

(2) \(13! + 2 \leq k \leq 13!+13\)


We need to determine whether k has a factor p such that 1<p<k, or in other words, whether k is a prime number. If it is, then it doesn’t have a factor between 1 and itself. If it isn’t, then it does.

Statement One Alone:
k > 4!

Since there are prime numbers greater than 4! and composite (non-prime) numbers greater than 4!, statement one alone is not sufficient to answer the question.

Statement Two Alone:
13! + 2 ≤ k ≤ 13! + 13

13! will have a factor of any integers from 2 to 13 inclusive. For any number k is, in the range of integers from 13! + 2 to 13! + 13 inclusive, k will have a factor from 2 to 13 inclusive. In particular, if k = 13! + n where (2 ≤ n ≤ 13), k will have n as a factor. For example, if k = 13! + 5, then k will have a factor of 5, since 5 divides into 13! and 5. If k = 13! + 8, then k will have a factor of 8 and hence a factor of 2.

Thus, statement two is sufficient to answer the question.

Answer: B
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Re: Does the integer k have a factor p such that 1 < p < k ?  [#permalink]

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New post 19 Aug 2019, 01:33
Hi Bunuel,

If we go with 2nd option then we can have multiple factors

For ex: If we take k=13!+4 then apart from 4, it will have others factors also .

So we will be getting more than one values of P.

So is it correct to mark B as sufficient answer.

Please Help.

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

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New post 19 Aug 2019, 01:45
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a12bansal wrote:
Hi Bunuel,

If we go with 2nd option then we can have multiple factors

For ex: If we take k=13!+4 then apart from 4, it will have others factors also .

So we will be getting more than one values of P.

So is it correct to mark B as sufficient answer.

Please Help.

Thanks


This is not a value question. The question is NOT what is the value of p.

It's an YES/NO question: Does the integer k have a factor p such that 1<p<k? And from (2) we get a definite YES answer to that question.

Hope it's clear.
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Re: Does the integer k have a factor p such that 1<p<k? 1.  [#permalink]

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New post 17 Oct 2019, 04:21
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Re: Does the integer k have a factor p such that 1<p<k? 1.   [#permalink] 17 Oct 2019, 04:21

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