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Number Properties and Divisibility

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by Bill@VeritasPrep » Sat Mar 31, 2012 6:50 pm
1) n could be 3, which is odd and divisible by 3, but it could also be 6, which is even and divisible by 3. Insufficient.

2) If n is 2, its factors are 1 and 2. 2n=4, and the factors of 4 are 1, 2, and 4. 3 factors is not twice as many as 2 factors, so n can't be even. If n is 3, its factors are 1 and 3. 2n=6, and the factors of 6 are 1, 2, 3, and 6. 4 factors is twice as many as 2 factors, so n must be odd.

You could also double-check with a non-prime odd. If n=9, then its factors are 1, 3, and 9. 2n=18, and the factors of 18 are 1, 2, 3, 6, 9, and 18. 6 factors is twice as many as 3 factors.
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by Anurag@Gurome » Sun Apr 01, 2012 9:17 pm
queenisabella wrote:Is the integer n odd?
(1) n is divisible by 3.
(2) 2n is divisible by twice as many positive integers as n.

OA is B.
I have posted a solution here: https://www.beatthegmat.com/is-the-integ ... 81868.html
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