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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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设n的最简质因数为a,b，n的因数组合为(1,a,b,ab)共4个。
2n的因数组合为(1,2,a,b,2a,2b,ab,2ab)共8个，这8个数不用去重的前提是2不等于a不等于b，所以a,b作为n的最简质因数一定是奇数，n是奇数。
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