prep里一道题，请教各位

hazardous

data sufficiency:is integer n odd? 1) n is divisible by 3   (2)2n is divisible by twice as many positive integers as n.

卮言浅夏

(1) not sufficient, for example, n = 6. (2) sufficient. if n is odd and has

x(1), x(2), . . . x(m) factors, then 2n will have twice as many factors: x(1),

x(2), . . . x(m); 2*x(1), 2*x(2), . . . 2*x(m)

卮言浅夏

For condition (2), if n is even, then n has at least two factors: 1 and 2,

plus the rest possible factors. However in the case of 2n, among the additional

NEW factors, there will be ANOTHER 2 (courtesy of 2*1), which is abundant.  So

if n is even, 2n could not have twice as many factors as n.