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

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

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27 Jan 2020, 01:49
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45% (medium)

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73% (00:59) correct 27% (01:02) wrong based on 14 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: If z is a positive integer, does z have more than 2 positive integer  [#permalink]

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27 Jan 2020, 04:36
The question is just asking if z is not prime, and there are no primes strictly between 23 and 29, so Statement 1 is sufficient. Statement 2 is not, since some odd numbers are prime and some are non-prime, so the answer is A.
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If z is a positive integer, does z have more than 2 positive integer  [#permalink]

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27 Jan 2020, 04:40
If z is a positive integer, does z have more than 2 positive integer factors?:
the question can be reduced to " is z a prime number "?

1)23 < z < 29
z can be 24, 25, 26, 27, 28
as none of these possible values of z is prime, we can definitely answer that z is not a prime number .
SUFFICIENT

2) z is odd: z can be any odd number : 3 or 9. hence it is NOT SUFFICIENT to answer whether z a prime number.

Bunuel wrote:
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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If z is a positive integer, does z have more than 2 positive integer  [#permalink]

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27 Jan 2020, 06:43
Bunuel wrote:
If z is a positive integer, does z have more than 2 positive integer factors?

(1) 23 < z < 29

(2) z is odd.

CONCEPT: Prime Numbers have exactly 2 distinct factors. FIrst factor being 1 and the second factor being the number itself

Any positive integer other than prime numbers and 1 have greater than 2 factors

Question: does z have more than 2 positive integer factors?

Question REPHRASED: Is z a Prime Number?

Statement 1: 23 < z < 29

i.e. z = {24, 25, 26, 27, 28} (because z is integer)
Not none of the possible values of z is a Prime number i,e, answer to teh question is is DEFINITELY NO hence
SUFFICIENT

Statement 2: z is odd

i.e. z may be 3 (prime) or 15 (non-prime) hence
NOT SUFFICIENT

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If z is a positive integer, does z have more than 2 positive integer   [#permalink] 27 Jan 2020, 06:43
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