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题库 / Prep2007E2-DS-21
Is the integer n odd?
(1) n is divisible by 3.
(2) 2n is divisible by twice as many positive integers as n.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
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2n因子数是n的2倍
n*k：如果k之前不是n的因子的话，相乘以后，n的所有因子乘以a都会形成一个新的因子，所以n*k的因子个数是n的因子个数的2倍。(1,a,b,n)-->(1,a,b,n,k,ka,kb,kn)，a*b=n
k之前是n的因子的话，因为新增加的k*之前不是k的因子=之前的因子k*之前不是k的因子，所以增加的因子数不等于增加前因子数的2倍。(1,a,k,n)-->(1,a,k,n,k,ka,k^2,kn), k*a=n，所以只有(1,a,k,n,k,k^2,kn)作为因子。
总结：If kn is divisible by twice as many positive integers as n, then n isn't divisible by k.
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