Is the integer n odd?
1) n is divisible by 3
2) 2n is divisible by twice as many positive integers as n

(1) is clearly insufficient. (3: yes; 6: no.)

as for (2), that's much more difficult.

there's only one way that 2n could be divisible by twice as many positive integers as n itself. here's how that would work:
for every factor of n, the multiplication by 2 would create a NEW factor of 2n (i.e., a number that is NOT already a factor of n).
this could only happen if NONE of the factors of n contains a '2' in its prime factorization.
if that's true, then n is odd.
therefore n must be odd.

the answer should be (b).

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Taking another route :

Stmt 2: Indicates that factors of 2n = 2(factors of n)

N = (2,3,4,5,6,7,8…..)

If n= 2…factors – 2.

2n = 4….facors - 3

i.e. (n is not 2)

If n= 3   fact – 2

2n = 6    fact – 4

If n= 5   fact – 2

2n = 10    fact – 4

If n= 7   fact – 2

2n = 14   fact – 4

Suff.