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# If x is a positive integer, is x prime?

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

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24 Nov 2007, 08:07
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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.

(2) x has the same number of factors as z, where z is a positive integer greater than 2.
[Reveal] Spoiler: OA

Last edited by Bunuel on 02 Apr 2014, 04:52, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.

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24 Nov 2007, 08:53
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I will go with A..

all prime factors have even number of factors i.e 2

any square of a positive integer will give you odd factors..sufficient..x is not a prime.

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Re: Is x prime? [#permalink]

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24 Nov 2007, 09:15
tarek99 wrote:
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.

(2) x has the same number of factors as z, where z is a positive integer greater than 2.

Its A for me too..It cant be a prime number....

X = has the same factors as y^2..

y = Y*Y so the factors of Y^2 = are 1, y and Y*Y for a number to be prime the only factors are 1 and itself.

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17 Dec 2007, 09:37
said A for this one.

y^2 = 9,16,25,36 and so on.

All these numbers have more than two factors, and so x cannot be prime.

B says z=3,4,5,6 and so on. Some of the numbers are prime, and some are not, so this statement by itself is insufficient.

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Re: Is x prime? [#permalink]

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17 Dec 2007, 11:19
tarek99 wrote:
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.

(2) x has the same number of factors as z, where z is a positive integer greater than 2.

A.

1) an integer^2 that is greater than 1 will always have more factors than a prime. So X is not a prime.

2) could be prime or could not be. Insuff.

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Re: If X is a positive integer, is x prime? (1) x has the same [#permalink]

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02 Apr 2014, 01:29
Bunuel,

I am still not clear with the questions solution. Can you Please throw Insight. Thanks!
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Re: If X is a positive integer, is x prime? (1) x has the same [#permalink]

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02 Apr 2014, 04:58
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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.

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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.

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

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

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16 Jan 2015, 07:38
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thorinoakenshield wrote:
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.

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.

Does this make sense?
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Re: If x is a positive integer, is x prime? [#permalink]

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17 Mar 2016, 06:26
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Re: If x is a positive integer, is x prime?   [#permalink] 17 Mar 2016, 06:26
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# If x is a positive integer, is x prime?

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