GMAT一道数学题(data sufficiency)Is the integer n odd?(1)n is divisible by 3(2)2n is divisible by twice as many as positive integers as n

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GMAT一道数学题(data sufficiency)
Is the integer n odd?
(1)n is divisible by 3
(2)2n is divisible by twice as many as positive integers as n

(1)不一定,比如6
(2)n一定是奇数.
如果n是奇数,那么2n的因子的数量是 n的因子的数量 的2倍.如果是偶数,则不然.
证明不写了,给你举个例子
比如 n=21
它的因子为 1,3,7,21,总共4个
2n的因子为 1,2,3,6,7,14,21,42,总共8个
再比如 n=6
它的因子为 1,2,3,6,总共4个
2n的因子为 1,2,3,4,6,12,总共6个