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Re: If X is a positive integer, is x prime? (1) x has the same [#permalink]
02 Apr 2014, 03:58
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I am still not clear with the questions solution. Can you Please throw Insight. Thanks!
If x is a positive integer, is x prime?
(1) x has the same number of factors as y^2, where y is a positive integer greater than 2.
y^2 is a perfect square. The number of distinct factors of a positive perfect square is ALWAYS ODD, while the number of factors of a prime is two (1 and itself). Thus since x has the same number of factors as a perfect square it cannot be a prime. Sufficient.
(2) x has the same number of factors as z, where z is a positive integer greater than 2. Clearly insufficient.