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If X is greater than two, is X the square of an odd prime integer?

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If X is greater than two, is X the square of an odd prime integer?  [#permalink]

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New post 25 Jun 2016, 23:23
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If X is greater than two, is X the square of an odd prime integer?

(1) X has exactly one composite number as factor.
(2) X has odd number of factors.

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Re: If X is greater than two, is X the square of an odd prime integer?  [#permalink]

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New post 26 Jun 2016, 01:58
1
we know
x>2 &
A composite number is any number that has more than two factors.

S1 - X has exactly one composite number as factor
S2 - A prime number has exactly two factors, 1 and itself

source of the question is?
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Re: If X is greater than two, is X the square of an odd prime integer?  [#permalink]

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New post 26 Jun 2016, 03:03
Hi Abhishek,

Thanks for the response.

The source of the question is from the CAT that I took from one of the coaching centre recently.


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Re: If X is greater than two, is X the square of an odd prime integer?  [#permalink]

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New post 23 Sep 2017, 00:41
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susheelh wrote:
If X is greater than two, is X the square of an odd prime integer?

(1) X has exactly one composite number as factor.
(2) X has odd number of factors.


Statement 1: this implies that x is a square of a prime number. but it could be an Odd prime square such as 9 whose only composite factor is 9 or it could be 4. Hence Insufficient

Statement 2: implies that x is a perfect square. but again x can be an odd or even perfect square. Hence Insufficient

Combining statement 1 & 2: we cannot determine whether x is 4 or x is square of any odd prime number. Hence Insufficient

Option E
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Re: If X is greater than two, is X the square of an odd prime integer?  [#permalink]

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New post 26 Nov 2017, 02:35
niks18 wrote:
susheelh wrote:
If X is greater than two, is X the square of an odd prime integer?

(1) X has exactly one composite number as factor.
(2) X has odd number of factors.


Statement 1: this implies that x is a square of a prime number. but it could be an Odd prime square such as 9 whose only composite factor is 9 or it could be 4. Hence Insufficient

Statement 2: implies that x is a perfect square. but again x can be an odd or even perfect square. Hence Insufficient

Combining statement 1 & 2: we cannot determine whether x is 4 or x is square of any odd prime number. Hence Insufficient

Option E


Hi niks18,

How come statement1 imply, x is square of a prime number?

because square of a prime number will have two composite factors, {1 and value itself}. Only prime number will have one composite number as factor which is 1.
so, is n't statement1 implying that x is prime number rather than a square of a prime number?

Thanks
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Re: If X is greater than two, is X the square of an odd prime integer?  [#permalink]

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New post 26 Nov 2017, 02:55
hellosanthosh2k2 wrote:
niks18 wrote:
susheelh wrote:
If X is greater than two, is X the square of an odd prime integer?

(1) X has exactly one composite number as factor.
(2) X has odd number of factors.


Statement 1: this implies that x is a square of a prime number. but it could be an Odd prime square such as 9 whose only composite factor is 9 or it could be 4. Hence Insufficient

Statement 2: implies that x is a perfect square. but again x can be an odd or even perfect square. Hence Insufficient

Combining statement 1 & 2: we cannot determine whether x is 4 or x is square of any odd prime number. Hence Insufficient

Option E


Hi niks18,

How come statement1 imply, x is square of a prime number?

because square of a prime number will have two composite factors, {1 and value itself}. Only prime number will have one composite number as factor which is 1.
so, is n't statement1 implying that x is prime number rather than a square of a prime number?

Thanks


Hi, 1 is neither prime nor composite. Composite number has more than one factor but 1 has only one factor ie. itself

As statement 1 says X has only one composite factor so it has to be a prime no because a composite no will have more than one composite factors

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Re: If X is greater than two, is X the square of an odd prime integer? &nbs [#permalink] 26 Nov 2017, 02:55
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