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题库 / Prep2007E1-DS-93
If the integer n is greater than 1, is n equal to 2 ?
(1) n has exactly two positive factors.
(2) The difference of any two distinct positive factors of n is odd.
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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n−1=oddn−1=odd --> n=odd+1=evenn=odd+1=even. Can nn be even number more than 2? No, because if n=even>2n=even>2 it obviously has 2 as a factor and again as "the difference of any two distinct positive factors of n is odd", then n-2 must be odd, but n−2=even−2=even≠oddn−2=even−2=even≠odd. Hence n=2n=2. Sufficient.
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