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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.

Re: If x is a positive integer, is x prime? [#permalink]

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16 Jan 2015, 07:06

Bunuel wrote:

honchos wrote:

Bunuel,

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.

Answer: A.

Hi there,

Can you please explain the statement "The number of distinct factors of a positive perfect square is ALWAYS ODD"? e.g. distinct factors of 36 are 2 and 3 (=even). Likewise for 100 are 2 and 5 ( = even).

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.

Answer: A.

Hi there,

Can you please explain the statement "The number of distinct factors of a positive perfect square is ALWAYS ODD"? e.g. distinct factors of 36 are 2 and 3 (=even). Likewise for 100 are 2 and 5 ( = even).

Thank you,

TO

It says distinct factors, not distinct prime factors.

So, for example, distinct factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36: 9 factors. Distinct factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100: 9 factors. Distinct factors of 4 are 1, 2, and 4: 3 factors.

Re: If x is a positive integer, is x prime? [#permalink]

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17 Mar 2016, 06:26

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