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Is a positive integer x a prime number?

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Is a positive integer x a prime number?  [#permalink]

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New post 04 Aug 2016, 19:25
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Question Stats:

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Is a positive integer x a prime number?
1) All the prime factors of x are greater than √x
2) All the prime factors of x are 1 and itself

*An answer will be posted in 2 days.

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Re: Is a positive integer x a prime number?  [#permalink]

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New post 05 Aug 2016, 04:40
I think the second point should be, "All the factors of x are 1 and itself". Since 1 is not a prime.


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Re: Is a positive integer x a prime number?  [#permalink]

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New post 05 Aug 2016, 10:39
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MathRevolution wrote:
Is a positive integer x a prime number?
1) All the prime factors of x are greater than √x
2) All the prime factors of x are 1 and itself

*An answer will be posted in 2 days.


Answer is D.

1) For every non prime number, its prime factors are either < or = or > then its root. Take any non prime no. , lets say 10. Prime factors are 2 and 5. sqrt(10) >3, but 2 is less than 3. Hence proved. Thus, Statement 1 is sufficient.

2) This is the definition of prime numbers.

Hence, D.
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Re: Is a positive integer x a prime number?  [#permalink]

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New post 08 Aug 2016, 18:19
The original condition has 1 variable (x) and there is a high chance that D is the correct answer. Con 1) and con 2) both are the definition of prime number. Hence, the correct answer is D.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
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Re: Is a positive integer x a prime number?  [#permalink]

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New post 16 Oct 2016, 03:55
abhimahna wrote:
MathRevolution wrote:
Is a positive integer x a prime number?
1) All the prime factors of x are greater than √x
2) All the prime factors of x are 1 and itself

*An answer will be posted in 2 days.


Answer is D.

1) For every non prime number, its prime factors are either < or = or > then its root. Take any non prime no. , lets say 10. Prime factors are 2 and 5. sqrt(10) >3, but 2 is less than 3. Hence proved. Thus, Statement 1 is sufficient.

2) This is the definition of prime numbers.

Hence, D.


Isn't statement no.2 just ridiculous ?
How on earth can 1 be regarded as a "PRIME NUMBER"

One is neither Prime nor Composite.
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Re: Is a positive integer x a prime number?  [#permalink]

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New post 16 Oct 2016, 04:18
stonecold wrote:
Isn't statement no.2 just ridiculous ?
How on earth can 1 be regarded as a "PRIME NUMBER"

One is neither Prime nor Composite.


No, it is not at all ridiculous

Definition of Prime Number

A Prime number is a natural number with exactly two distinct natural number divisors: 1 and itself. Otherwise a number is called a composite number. Therefore, 1 is not a prime, since it only has one divisor, namely 1. A number n>1 is prime if it cannot be written as a product of two factors a and b, both of which are greater than 1: n = ab.


Statement 2 is sufficient to state the x is a prime number...
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Re: Is a positive integer x a prime number?  [#permalink]

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New post 16 Oct 2016, 04:35
Abhishek009 wrote:
stonecold wrote:
Isn't statement no.2 just ridiculous ?
How on earth can 1 be regarded as a "PRIME NUMBER"

One is neither Prime nor Composite.


No, it is not at all ridiculous

Definition of Prime Number

A Prime number is a natural number with exactly two distinct natural number divisors: 1 and itself. Otherwise a number is called a composite number. Therefore, 1 is not a prime, since it only has one divisor, namely 1. A number n>1 is prime if it cannot be written as a product of two factors a and b, both of which are greater than 1: n = ab.


Statement 2 is sufficient to state the x is a prime number...



Completely Disagree..!!!

How can someone say that 1 is a prime factor of a number.
One is neither prime nor composite.
In a way your statement is supporting my claim :)

statement 2 states => All the prime factors of x are 1 and itself.
How can one be a prime factor
The statement should be => All the factors of x are 1 and itself.
Big Difference :)
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Re: Is a positive integer x a prime number?  [#permalink]

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New post 16 Oct 2016, 10:22
stonecold wrote:
Abhishek009 wrote:
stonecold wrote:
Isn't statement no.2 just ridiculous ?
How on earth can 1 be regarded as a "PRIME NUMBER"

One is neither Prime nor Composite.


No, it is not at all ridiculous

Definition of Prime Number

A Prime number is a natural number with exactly two distinct natural number divisors: 1 and itself. Otherwise a number is called a composite number. Therefore, 1 is not a prime, since it only has one divisor, namely 1. A number n>1 is prime if it cannot be written as a product of two factors a and b, both of which are greater than 1: n = ab.


Statement 2 is sufficient to state the x is a prime number...



Completely Disagree..!!!

How can someone say that 1 is a prime factor of a number.
One is neither prime nor composite.
In a way your statement is supporting my claim :)

statement 2 states => All the prime factors of x are 1 and itself.
How can one be a prime factor
The statement should be => All the factors of x are 1 and itself.
Big Difference :)


Yes, I agree. I missed that point. My Bad.

1 is a factor of a prime number BUT NOT a prime factor. 1 is neither prime nor composite.

Either the OA marked is incorrect or the question is incorrect.

Thanks stonecold :-D
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Re: Is a positive integer x a prime number?  [#permalink]

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New post 22 Dec 2018, 05:13
abhimahna wrote:
MathRevolution wrote:
Is a positive integer x a prime number?
1) All the prime factors of x are greater than √x
2) All the prime factors of x are 1 and itself

*An answer will be posted in 2 days.


Answer is D.

1) For every non prime number, its prime factors are either < or = or > then its root. Take any non prime no. , lets say 10. Prime factors are 2 and 5. sqrt(10) >3, but 2 is less than 3. Hence proved. Thus, Statement 1 is sufficient.

2) This is the definition of prime numbers.

Hence, D.


Hi abhimahna

Request you to please elaborate with one more example. I am not able to understand this solution. Many thanks
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Re: Is a positive integer x a prime number?   [#permalink] 22 Dec 2018, 05:13
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