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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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New post Updated on: 02 Apr 2014, 04:52
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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.

Originally posted by tarek99 on 24 Nov 2007, 08:07.
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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Re: If X is a positive integer, is x prime? (1) x has the same  [#permalink]

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New post 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.

Answer: A.
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New post 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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New post 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.



When choosing your answer, please provide your explanation.


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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New post 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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New post 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.



When choosing your answer, please provide your explanation.



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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New post 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?  [#permalink]

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New post 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).

Thank you,

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

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New post 16 Jan 2015, 07:38
1
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.

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.

Does this make sense?
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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New post 29 Jun 2018, 04:40
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.

1) SUFF.: If x has the same number of factors as y2, then x cannot be prime. A prime number is a number that has only itself and 1 as factors. But a square has at least 3 prime factors. For example, if y is prime, y = 2, then y2 = 4, which has 1, 2, and 4 as factors. If the root (in this case y) is not prime, then the square will have more than 3 factors. For example, if y = 4, then y2 = 16, which has 1, 2, 4, 8, and 16 as factors. In either case, x will have at least 3 factors, establishing it as nonprime.

(2) INSUFF.: If z is prime, then x will have only two factors, making it prime. But if z is nonprime, it will have either one (if z = 1) or more than two factors, which means x will have either one or more than two factors, making x nonprime. Since we do not know which case we have, we cannot tell whether x is prime
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Re: If x is a positive integer, is x prime? &nbs [#permalink] 29 Jun 2018, 04:40
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