In order for xy to be greater than zero, x and y must have the same sign. So the prompt question can be reworded as do x and y have the same sign.theabster wrote:Line L passes through points R (0, -5 ) and S (4,0). Point P with coordinates (x, y) is a point on Line L. Is xy > 0?
(1) x>4 (2) y>-5
Attached is the question
This is a data sufficiency question
(1) Sufficient. All points on Line L, such that x>4, have a positive y coordinate. Since x and y are both positive, their product is greater than zero.
(2) Not sufficient. If y > -5, then x will always be positive. Since x and y could have the same sign, or could have different signs, we cannot determine whether the product is greater than zero.
Answer: A
Edit: Originally, I had misread your second condition as y<-5. If y<-5, then (2) would also be sufficient. Since it's actually y > -5, this is not sufficient. Because x will always be positive, for all y>-5, but y obviously could be negative (for all y, such that -5<y<0), y could be 0, or y could be greater than zero.
