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# If n is a positive integer, is n odd?

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Intern
Joined: 16 Nov 2013
Posts: 23
If n is a positive integer, is n odd?  [#permalink]

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Updated on: 29 Dec 2014, 03:00
00:00

Difficulty:

25% (medium)

Question Stats:

73% (00:49) correct 27% (00:53) wrong based on 94 sessions

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If n is a positive integer, is n odd?

(1) n has exactly two positive factors.

(2) n is different from 2

I am struggling with this question because i don't know whether to consider 1 as a positive factor itself.

Thank you in advance !

Originally posted by gmatmania17 on 29 Dec 2014, 02:50.
Last edited by Bunuel on 29 Dec 2014, 03:00, edited 1 time in total.
Edited the tags
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Joined: 02 Sep 2009
Posts: 53066
Re: If n is a positive integer, is n odd?  [#permalink]

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29 Dec 2014, 03:05
1
If n is a positive integer, is n odd?

(1) n has exactly two positive factors. This implies that n is a prime number. All primes but 2 are odd, so n can be 2, so even or any other odd prime. Not sufficient.

(2) n is different from 2. Clearly insufficient.

(1)+(2) Since n cannot be 2, then it's some odd prime. Sufficient.

As for your question: 1 is a factor of every integer. Check links below.

Theory on Number Properties: math-number-theory-88376.html
Tips on Number Properties: number-properties-tips-and-hints-174996.html

All DS Number Properties Problems to practice: search.php?search_id=tag&tag_id=38
All PS Number Properties Problems to practice: search.php?search_id=tag&tag_id=59

P.S. Please tag questions properly: this is a number properties question, not an algebra question. Also, I guess this is NOT a Self-made question as you've tagged.
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Re: If n is a positive integer, is n odd?  [#permalink]

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22 Aug 2016, 07:31
Here we need to find if n is even or odd
statement 1 => n is prime => n can be 2 or 3 or 5 etc => not suff
statement 2 => n can be 3 or 4 or 5 => not suff
combining them n must be odd as 2 is the only even prime and all primes except 2 are odd
SMASH that C
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Re: If n is a positive integer, is n odd?  [#permalink]

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27 Nov 2017, 11:09
1
Hi All,

We're told that N is a positive integer. We're asked if N is ODD. This is a YES/NO question and we can solve it by TESTing VALUES.

1) N has exactly two positive factors.

For N to have exactly 2 factors, N must be a PRIME number.
IF...
N=2, then the factors are 1 and 2 and the answer to the question is NO.
N=3, then the factors are 1 and 3 and the answer to the question is YES.
Fact 1 is INSUFFICIENT

2) N is different from 2.

N=3, then the answer to the question is YES.
N=4, then the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we know that N must be PRIME and that it cannot be 2. All of the remaining possibilities are ALL ODD, so the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

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Re: If n is a positive integer, is n odd?   [#permalink] 27 Nov 2017, 11:09
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# If n is a positive integer, is n odd?

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