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标题: prep里一道题，请教各位 [打印本页]

作者: hazardous 时间: 2010-11-29 07:00 标题: prep里一道题，请教各位

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

作者: 卮言浅夏 时间: 2010-11-29 20:49

(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)

作者: 卮言浅夏 时间: 2010-11-29 20:49

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.

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