P is an integer greater than one, but P is not a square of

Question

P is an integer greater than one, but P is not a square of an integer. Is P a prime number?

(1) The only factor of P that can be greater than square root p is p itself

(2) The only factor of P that can be less than square root p is 1.

FN · Answer

I m going with D

1) suppose for argument sake P=4

factors are 1, sqrt(4) , 4... but P= is a sqaure of an integer and thts not possible.. try 6, which is not a square of any number..factors are 1, 2, sqrt(6), 3, 6 ...again if P is not a prime there will always be a factor greater than sqr(P) but less than P.

so 1) is sufficient

2) lets pick p=8 (not a square of an integer)
there will always be a factor less than sqrt(P) but greater than 1

P has to be a prime for 2) to b sufficient

ashkrs · Answer

I think its E . 
Lets take the number 20 . The square root will be close to 4.5 
Now 20 has a factor 2 , 4 , 5 ,10
So we have factors which is greater than square root but not the number itself and less than the square root but not 1.

FN · Answer

sqrt(20)=2*Sqrt(5) which is greater than 2..so statement 2 says the only factor of P less than sqrt(P) is 1....

Ferihere · Answer

I have also D, 
small question why there is used  small p  in statement instead of  capital P ?

bkk145 · Answer

Thanks guys. 
OA=D
This one is kind of strange and took me some time.
About the big p and small p, I mistyped...they are all the same p. sorry.

KillerSquirrel · Answer

statement 1 If p=m*n than either m or n is greater then sqrt(p). sufficient statement 2 If p=m*n than either m or n is smaller than sqrt(p). sufficient the answer is (D)

P is an integer greater than one, but P is not a square of

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