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题库 / Prep2007E1-DS-3
How many different prime numbers are factors of the positive integer n ?
(1) Four different prime numbers are factors of ~$2n$~.
(2) Four different prime numbers are factors of ~$n^2$~.
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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(2) n²有四个不同的质因数就避免了(1)中出现的问题，n^2只有四个不同质数，由于只是n的二次方，就是全部数字的再一次相乘，因而质数是肯定的。假设 n²=2 ²3²5²7²，则n便含有四个不同的质因数(2、3、5、7) 因此(2)是充分的，此题选B
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