psm12se wrote:Is xy > 0 ?

1. x - y > -2
2. x - 2y < -6

(1) x - y > -2
If x = 4, y = 2, then x - y = 4 - 2 = 2, which is greater than -2. Here xy = 4 * 2 = 8 > 0.
If x = -1/2, y = 1/2, then x - y = -1/2 - 1/2 = -1, which is greater than -2. Here xy = (-1/2)(1/2) = -1/4 < 0.
No definite answer; NOT sufficient.

(2) x - 2y < -6
If x = 4, y = 6, then x - 2y = 4 - 12 = -8, which is less than -6. Here xy = 4 * 6 = 24 > 0.
If x = -4, y = 6, then x - 2y = -4 - 12 = -16, which is less than -6. Here xy = -4 * 6 = -24 < 0.
No definite answer; NOT sufficient.

Combining (1) and (2), y - 2 < x < 2y - 6.
So, y > 4 and x > y - 2 > 2
So, xy > 0; SUFFICIENT.

The correct answer is C.

psm12se wrote:Is xy > 0 ?

1. x - y > -2
2. x - 2y < -6

Is xy>0?

i. x-y>-2
ii. x-2y<-6

[/quote]
Target question: Is xy>0?

Statement 1: x-y > -2
There are several pairs of numbers that meet this condition. Here are two:
Case a: x = 5 and y = 1, in which case xy is greater than 0
Case b: x = 5 and y = -1, in which case xy is not greater than 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x - 2y < -6
There are several pairs of numbers that meet this condition. Here are two:
Case a: x = 1 and y = 5, in which case xy is greater than 0
Case b: x = -1 and y = 5, in which case xy is not greater than 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
Here's what we know:
x-y > -2
x-2y < -6

Since both inequalities have an x, let's isolate x in both of them to get:
y-2 < x
x < 2y-6

Aside: Notice that I rewrote them so that the 2 inequality symbols are pointing in the same direction.

Now we can combine these inequalities to get: y-2 < x < 2y-6
Next, remove the x to get: y-2 < 2y-6
Then subtract y from both sides and add 6 to both sides to get: 4 < y
Great, we now know that y is positive.
Also, if y-2 < x (and y>4), then we know that x must also be positive
Since we now know that x and y are positive, we can be certain that xy is greater than 0

So, the answer is C

Cheers,
Brent

Deepthi Subbu wrote:Hi Brent ,

I was able to narrow down to C and E . Suppose y>4 , lel me use this value in statement 2.
x-2y < -6 (Consider y=5)
=> x < 4.
But considering a greater value of y, say 12.
=> The value of x is positive.

In this case should we consider statement 1 ?

Everything you've said coincides with my earlier conclusions.
If y = 5, then it is true that x < 4
But this does not suggest that x can be negative.
If y = 5, then statement 1 tells us that x-5 > -2, which means x > 3
So, x and y are still both positive if y = 5.

I hope that helps.

Cheers,
Brent