Is XY>0?

[mschwrtz]

Ah, makes sense then.

[ifydaniel100]

Ron, I'm struggling to understand how the second statement proves that x is definitely positive. I follow that y>4 and I follow that x>2 if I only test equation (1). But I would think that I should be able to test either and come away with the fact that x is positive. However when I test equation (2) x proves to be positive or negative!

Testing equation (2) x - 2y < -6

since y>4
If y = 4.1, then x - 8.2 < -6 and x < 2.2 (this suggests x can be positive or negative)
If y = 6, then x - 12 < -6 and x < 6 (this suggests x can be positive or negative)
and so on...

I don't understand how we prove x is definitely positive if I test equation (2)

[tim]

as near as i can tell, several people have mentioned that the answer is C in this thread. when a data sufficiency answer is C, that means statement 2 will NOT give you a definitive answer. so your claim that x can be positive or negative is entirely consistent with the stated answer to the problem..

[ifydaniel100]

Thanks Tim. Just to make sure i'm on the same page, you are saying that when evaluating option C, we have our answer after evaluating only statement (1) because we are simply trying to prove the sign of x. Had we tested statement (2) first we would have determined that x could be either positive or negative and at that point would have had to evaluate statement (1) to find the x values that overlap with statement (2). In other words - Statement 1, x is positive. Statement (2), x is positive or negative. Overlap, x is positive.

[jlucero]

Here's what's tricky about having multiple inequalities and trying to plug in values. When you solve for the first variable, you are finding all cases that COULD work for that variable. But when you plug in the lower extreme (y=4) into each equation, you aren't guaranteed that any numbers will work with that particular variable. But remember that y>4, so let's say that y = 10. By plugging in values of y = 10, you learn from (1) that x > 8, and from (2) that x < 14. These two equations combine to give you a range for what x has to be if y is some particular value. That's why when you plugged in y = 2, you got a confusing answer- x can't be both greater and less than 2.

The key thing though, is once you discover that y > 4, the first equation (x + 2 > y) tells us that no matter how much smaller or larger y is than 4, x will have to be an even larger number. That guarantees that the product is positive.

Graphically, we can see this from the picture I took of a graphing calculator. Note that the only place where there is overlap in these two inequalities is in quadrant one, when both x and y are positive.