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

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.

(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.

It might be a good idea to work with the equation of the line.

Let's start by using the two coordinates given to find the slope:

m = (0 - (-5)) / (4 - 0) = 5/4

and we know the y-intercept is -5, so the equation of the line is

y = (5/4)x - 5

S1:

We're given x, so let's arrange the equation of the line in terms of x:

y = (5/4)x - 5

(5/4)x = y + 5

x = (4/5)y + 4

Since x > 4, we know that (4/5)y > 0, which forces y > 0. SUFFICIENT

S2:

y > -5

Since y = (5/4)x - 5, we can substitute that in:

(5/4)x - 5 > -5

(5/4)x > 0

So x > 0. But this DOESN'T tells us about y: we could have x = 1, y = -3.75, but we could also have x = 40 and y = 45. NOT SUFFICIENT