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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] New post 07 Mar 2012, 10:51
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Question Stats:

60% (02:09) correct 40% (00:55) wrong based on 141 sessions
If Z is an integer, is Z prime?

(1) 15! < Z
(2) 17! + 2 < Z < 17! + 17
[Reveal] Spoiler: OA
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Re: Is Z prime? [#permalink] New post 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*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.

Answer: B.

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

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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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