If Z is an integer, is Z prime? : GMAT Data Sufficiency (DS)
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# If Z is an integer, is Z prime?

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If Z is an integer, is Z prime? [#permalink]

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07 Mar 2012, 10:51
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If Z is an integer, is Z prime?

(1) 15! < Z
(2) 17! + 2 < Z < 17! + 17
[Reveal] Spoiler: OA
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If Z is an integer, is Z prime? [#permalink]

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07 Mar 2012, 11:01
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If Z is an integer, is Z prime?

(1) $$15!<z$$ --> $$z$$ is more than some number ($$15!$$). $$z$$ may or may not be a prime. Not sufficient.

(2) $$17!+2\leq{z}\leq{17!+17}$$ --> $$z$$ cannot be a prime. For instance if $$z=17!+13=13*(2*3*4*5*6*7*8*9*10*11*12*14*15*16*17+1)$$, then $$z$$ is a multiple of 13, so not a prime. Same for all other numbers in this range. So, $$z=17!+x$$, where $$2\leq{x}\leq{17}$$ will definitely be a multiple of $$x$$ (as we would be able to factor out $$x$$ out of $$17!+x$$, the same way as we did for 13). Sufficient.

Similar questions to practice:
if-x-is-an-integer-does-x-have-a-factor-n-such-that-100670.html
does-the-integer-k-have-a-factor-p-such-that-1-p-k-126735.html

Hope it's clear.
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Re: If Z is an integer, is Z prime? [#permalink]

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12 Jun 2013, 03:27
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: If Z is an integer, is Z prime? [#permalink]

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08 Jan 2014, 02:25
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If the statement B was rephrased to ===> 17! + 2 < Z < 17! + 19 then will the answer to this question change to E ?
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Re: If Z is an integer, is Z prime? [#permalink]

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09 Nov 2014, 10:03
For the above question, this will help (its a matched question and all the posts there make things clearer)
if-x-is-an-integer-does-x-have-a-factor-n-such-that
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Re: If Z is an integer, is Z prime? [#permalink]

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12 Sep 2016, 02:17
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: If Z is an integer, is Z prime? [#permalink]

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15 Nov 2016, 08:02
I read the Kaplan explanation and read explanations above in the thread and I can't find a clue....
For instance, why 17!+13 is equal to 13∗(2∗4∗5∗6∗7∗8∗9∗10∗11∗12∗14∗15∗16∗17+1)? Isn't (2∗4∗5∗6∗7∗8∗9∗10∗11∗12∗14∗15∗16∗17+1) = 17!? So, why 17! multiplied by 13 would be equal to 17! + 13?
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Re: If Z is an integer, is Z prime? [#permalink]

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15 Nov 2016, 08:08
Erjan_S wrote:
I read the Kaplan explanation and read explanations above in the thread and I can't find a clue....
For instance, why 17!+13 is equal to 13∗(2∗4∗5∗6∗7∗8∗9∗10∗11∗12∗14∗15∗16∗17+1)? Isn't (2∗4∗5∗6∗7∗8∗9∗10∗11∗12∗14∗15∗16∗17+1) = 17!? So, why 17! multiplied by 13 would be equal to 17! + 13?

17! + 13 = 2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17 + 13

Factor out 13: 13*(2*3*4*5*6*7*8*9*10*11*12*14*15*16*17 + 1)
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Re: If Z is an integer, is Z prime? [#permalink]

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15 Nov 2016, 08:30
Ok, now I can see.. But honestly, it is kind of hard question for somebody who did not specialize in math...
Re: If Z is an integer, is Z prime?   [#permalink] 15 Nov 2016, 08:30
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