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# If z is a positive integer, does z have more than 2 positive

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Manager
Joined: 18 Jun 2011
Posts: 50
If z is a positive integer, does z have more than 2 positive  [#permalink]

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20 Jun 2011, 20:46
1
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Difficulty:

25% (medium)

Question Stats:

70% (01:04) correct 30% (01:08) wrong based on 56 sessions

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If z is a positive integer, does z have more than 2 positive integer factors?

(1) 23 < z < 29

(2) z is odd.
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Re: Tricky DS - Factors based problem  [#permalink]

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20 Jun 2011, 22:26
The question is asking whether z is a prime

(1) 23 < z < 29

z can be 25,26,27,28, all of which are composite numbers so Sufficient

(2) z is odd.

Not Sufficient as z can be 3 (Prime) or 9 (Composite)

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Manager
Joined: 16 Mar 2011
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Re: Tricky DS - Factors based problem  [#permalink]

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21 Jun 2011, 01:01
A indeed.

Statement 1: Z can be 24,25,26,27,28, having factors of respectively: 2^3(3), 5^2, 2(13), 3^3, 7(2^2),

as you can see no value for Z has more than 2 different integer factors.

Statement 2: insufficient. Z could be anything. Z could be 15, having 2 different factors. But it could alsof be 105 having 3 different factors (3,5,7).
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Re: Tricky DS - Factors based problem  [#permalink]

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23 Jun 2011, 03:34
a all integers between 23 and 29 have more than 2 factors. Sufficient.

b 1,3,9 give different values. Not sufficient.

A it is.
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Joined: 19 Apr 2011
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Re: Tricky DS - Factors based problem  [#permalink]

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24 Jun 2011, 03:20
23 < z < 29
No prime numbers in the range above So all have more than 2 factors Sufficient
Some odd numbers are prime some are non prime
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Re: If z is a positive integer, does z have more than 2 positive  [#permalink]

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10 Aug 2017, 02:54
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Re: If z is a positive integer, does z have more than 2 positive   [#permalink] 10 Aug 2017, 02:54
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