The GMAT would restrict this problem to POSITIVE integers:

Is the positive integer n odd?

1. n is divisible by 3.
2. 2n divisible by twice as many +ve integers as n.

OA is B

Statement 1: n is divisible by 3.
Since it's possible that n=3 or that n=6, INSUFFICIENT.

Statement 2: 2n is divisible by twice as many positive integers as n.
No even integer satisfies this constraint.
If n=2 (which is divisible by 1 and 2, for a total of 2 factors), then 2n=4 (which is divisible by 1, 2 and 4, for a total of 3 factors).
If n=4 (which is divisible by 1, 2 and 4, for a total of 3 factors), then 2n=8 (which is divisible by 1, 2, 4 and 8, for a total of 4 factors).
If n=6 (which is divisible by 1, 2, 3 and 6, for a total of 4 factors), then 2n=12 (which is divisible by 1, 2, 3, 4, 6, and 12, for a total of 6 factors).
In none of these cases does 2n have twice as many factors as does n.
Since no even value satisfies statement 2, n must be ODD.
SUFFICIENT.

The correct answer is B.

GMATGuruNY wrote:The GMAT would restrict this problem to POSITIVE integers:

Is the positive integer n odd?

1. n is divisible by 3.
2. 2n divisible by twice as many +ve integers as n.

OA is B

Statement 1: n is divisible by 3.
Since it's possible that n=3 or that n=6, INSUFFICIENT.

Statement 2: 2n is divisible by twice as many positive integers as n.
No even integer satisfies this constraint.
If n=2 (which is divisible by 1 and 2, for a total of 2 factors), then 2n=4 (which is divisible by 1, 2 and 4, for a total of 3 factors).
If n=4 (which is divisible by 1, 2 and 4, for a total of 3 factors), then 2n=8 (which is divisible by 1, 2, 4 and 8, for a total of 4 factors).
If n=6 (which is divisible by 1, 2, 3 and 6, for a total of 4 factors), then 2n=12 (which is divisible by 1, 2, 3, 4, 6, and 12, for a total of 6 factors).
In none of these cases does 2n have twice as many factors as does n.
Since no even value satisfies statement 2, n must be ODD.
SUFFICIENT.

The correct answer is B.

How about when n = say 18 and there are 6 factors and 2*n is 36 which is divisible by 9 factors ?

mgm wrote:

GMATGuruNY wrote: Statement 2: 2n is divisible by twice as many positive integers as n.
No even integer satisfies this constraint.
If n=2 (which is divisible by 1 and 2, for a total of 2 factors), then 2n=4 (which is divisible by 1, 2 and 4, for a total of 3 factors).
If n=4 (which is divisible by 1, 2 and 4, for a total of 3 factors), then 2n=8 (which is divisible by 1, 2, 4 and 8, for a total of 4 factors).
If n=6 (which is divisible by 1, 2, 3 and 6, for a total of 4 factors), then 2n=12 (which is divisible by 1, 2, 3, 4, 6, and 12, for a total of 6 factors).
In none of these cases does 2n have twice as many factors as does n.
Since no even value satisfies statement 2, n must be ODD.
SUFFICIENT.

The correct answer is B.

How about when n = say 18 and there are 6 factors and 2*n is 36 which is divisible by 9 factors ?

This example supports the conclusion that no even integer will satisfy statement 2.
If n=18, then 2n=36 does NOT have twice as many factors as does n.

We could certainly come up with a proof that shows conclusively why no even integer will satisfy statement 2, but on test day I wouldn't bother.

N=ODD?

Statement 1: 6, 3 -- NOT SUFFICIENT
Statement 2: Its a rule -- "ODD Number multiplied by 2 will have exactly double the factor" SUFFICIENT

Answer [spoiler]{B}[/spoiler]

I find the language used in the question ambiguous:

(2)2n divisible by twice as many +ve integers as n

I think it should read:
"2n divisible by twice as many +ve integers as does n"

Else, possible interpretations:
(a)2n has twice as many factors as "n"
(b)2n has twice as many factors as does "n"

Does anyone see the dilemma here?

peter456 wrote:I find the language used in the question ambiguous:

(2)2n divisible by twice as many +ve integers as n

I think it should read:
"2n divisible by twice as many +ve integers as does n"

Else, possible interpretations:
(a)2n has twice as many factors as "n"
(b)2n has twice as many factors as does "n"

Does anyone see the dilemma here?

I"ll be glad to hear from others on the issue of ambiguity I raised above