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If n is a positive integer, is n odd?

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by BTGmoderatorLU » Wed Nov 01, 2017 10:02 am
If n is a positive integer, is n odd?

(1) n has exactly two positive factors.

(2) n is different from 2.

The OA is C.

I am struggling with this question because I don't know whether to consider 1 as a positive factor itself. Please, can any expert assist me with it? Thanks.
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Source: — Data Sufficiency |

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by [email protected] » Wed Nov 01, 2017 12:46 pm
Hi LUANDATO,

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

Final Answer: C

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Rich
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