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If n is a positive integer and is not the square of any integer, is it

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If n is a positive integer and is not the square of any integer, is it [#permalink]

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New post 05 Oct 2017, 05:10
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If n is a positive integer and is not the square of any integer, is it a prime number?

(1) Among the factors of n, only n is greater than √n
(2) Among the factors of n, only 1 is less than √n

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Re: If n is a positive integer and is not the square of any integer, is it [#permalink]

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New post 05 Oct 2017, 05:35
Bunuel wrote:
If n is a positive integer and is not the square of any integer, is it a prime number?

(1) Among the factors of n, only n is greater than √n
(2) Among the factors of n, only 1 is less than √n


Question : Is n a Prime Number ?

Statement 1: Among the factors of n, only n is greater than √n
Every number can be written as product of two numbers e.g. 100 = 1*100 or 2*50 etc
But Prime numbers have only two distinct factors i.e. 1 and the number itself
Also, a number n is called prime if no prime number smaller than √n can divide the number n
and if there is no factor of n bigger than √n then there will be no factor of the number smaller than √n except 1 hence there are only two factors of the number 1 and number itself
P.S. It's already mentioned that the number is not a perfect square
SUFFICIENT

Statement 2: Among the factors of n, only 1 is less than √n
Same explanation as mentioned in statement 1 follows Hence
SUFFICIENT


Answer: Option D

Each statement is sufficient to answer
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If n is a positive integer and is not the square of any integer, is it [#permalink]

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New post 05 Oct 2017, 23:50
Total Factors of a Prime Number are exactly two : number itself and one.

St.1: As n is greater than √n, n cannot be equal to 1 and hence, total factors of n are atleast more than two [n,√n,1..]. Therefore, n is not a prime number.: SUFFICIENT

St.2: Similarly, √n is greater than 1. n cannot be equal to 1 and hence, total factors of n are atleast more than two. Therefore, n is not a prime number.: SUFFICIENT

Ans D

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If n is a positive integer and is not the square of any integer, is it   [#permalink] 05 Oct 2017, 23:50
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If n is a positive integer and is not the square of any integer, is it

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