Statement 2) says that X is greater than Y and that they have the same sign (negative or positive)
This quote is incorrect. X > Y only if both are positive. For example if x = 3 and y =2, then x/y = 3/2.
However, if both x and y are negative, then x < y. For example, if x = -3 and y = -2, then x / y = 3/2. Here, x < y.
So (2) basically states that x > y > 0 or x < y < 0. (1) states that x > y, so then they must both be positive. Hope that makes sense.