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Statement 2 is the another rendition of statement 1. Essentially, if the two number have no divisors in common except 1, they are two unique numbers (say 2,3 or 2,9).

1) x and y are different.. x>0 y>0 sufficient try any number sum>2 2) GCD=1..tells me that x and Y are different either odd or even or different primes...sufficient

In the question - Stt2: X and Y are integers which do not have common divisors except 1 Since, 1 and 1 are integers which do not have common divisors except 1 So, this will be insufficient.

When X and Y are different, x/y + y/x is always bigger than 2. This is because (x-y)^2 >0 , from where x^2 + y^2 > 2xy . After dividing by XY we get x/y + y/x >2 .

S_2 alone is not sufficient. The answer is NO if X = Y = 1. _________________