prep里一道题，请教各位

kw891711

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

kw891711

没人帮忙看看吗？？

sdcar2010

(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)

sdcar2010

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.