AJ2009 wrote:If x is a positive integer greater than 1, does x have any integer factor n such that 1 < n < x ?

(1) x is even.

(2) 47 < x < 53

I say (B)

(1) IS NOT SUFFICIENT because 2 is even, but has no factor greater than 1 and less than 2.
(2) IS SUFFICIENT

48 --> 16 is a factor of 48
49 --> 7 is a factor of 49
50 --> 5 is a factor of 50
51 --> 17 is a factor of 51
52 --> 26 is a factor of 52

If 48-52 contained a prime number, then this would NOT be sufficient. (C) would be the right answer.

q: if x>1, does x have any integer factor n such that 1 < n < x ?
ie of all the factors of x is there a smaller factor n such that 1 < n < x?

I guess this is my attempt to rephrase the questn. I am not sure if this is correct or not.

(i) x is even
=> Insuff. because if x=2 then
Factors of 2=2x1
there is no smaller factor of 2 other than 1 which cannot be taken into account because x>1

, [C], or [E]

(ii) 47 < x < 53
x=48, 49, 50, 51, or 52
=> if x=48, then Factors of 48=2x2x2x2x3
Hence there is a factor n=2 which is less than 48

llly, if x=49, then factors of 49=7x7
Hence there is a factor n=7 which is less than 49

Hence Suff.

Is this OA?

Agree with B

Stmt I

x=2 the answer is no
x= 4 the answer is yes

INSUFF

Stmt II

Since x is an integer 48,49,50,51,52 satisfy 47<x<53 and all these x's have factors n's such that 1<n<x since they are not prime

SUFF

Choose B

Regards,
CR

agree B is the ans