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

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

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25 Jun 2011, 23:23
00:00

Difficulty:

45% (medium)

Question Stats:

67% (00:31) correct 33% (01:11) wrong based on 12 sessions

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Does the integer k have a factor p such that 1 = 4!
2. 13! + 2 =< k =< 13! + 13

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Satyameva Jayate - Truth alone triumphs

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

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25 Jun 2011, 23:24
can somebody please explain me this?
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Satyameva Jayate - Truth alone triumphs

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

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26 Jun 2011, 00:21
harshavmrg wrote:
can somebody please explain me this?

It's asked whether K is a prime number or no.
from 1) K might equal $$27$$ (and it has such factors as 3 or 9) or it can be $$29$$ (prime number without factors we need)
ins
(2)
write it in this way:
$$2*(1*3*4*...*13+1)<=K<=13*(1*2*3*...*12+1)$$
Now we see you can write any number fro this interval in such form.
Example: $$13!+7=7*(1*2*3*4*5*6*8*...*13+1)$$
we do have a factor that we ask to find.
So, it's (B).
Math Expert
Joined: 02 Sep 2009
Posts: 47019
Re: Does the integer k have a factor p such that 1 < p < k [#permalink]

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04 Dec 2017, 03:32
Does the integer k have a factor p such that 14![/m] --> $$k$$ is more than some number ($$4!=24$$). $$k$$ may or may not be a prime. Not sufficient.

(2) $$13!+2\leq{k}\leq{13!+13}$$ --> $$k$$ can not be a prime. For instance if $$k=13!+8=8*(2*4*5*6*7*9*10*11*12*13+1)$$, then $$k$$ is a multiple of 8, so not a prime. Same for all other numbers in this range. So, $$k=13!+x$$, where $$2\leq{x}\leq{13}$$ will definitely be a multiple of $$x$$ (as we would be able to factor out $$x$$ out of $$13!+x$$, the same way as we did for 8). Sufficient.

Check similar question: http://gmatclub.com/forum/factor-factorials-100670.html

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http://gmatclub.com/forum/does-the-inte ... 26735.html

If anything remains unclear please continue discussion there.

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: Does the integer k have a factor p such that 1 < p < k   [#permalink] 04 Dec 2017, 03:32
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