Data Sufficiency

Is XY > 0?

(1) X - Y > -2
(2) X - 2Y < -6

tonebeeze wrote:Is XY > 0?

(1) X - Y > -2
(2) X - 2Y < -6

Statement 1: x > y-2
If y=2 and x= 1, is 1*2 > 0? Yes.
If y= -1 and x = 1, is 1*(-1) > 0? No.
Since the answer can both Yes and No, insufficient.

Statement 2: x < 2y-6
If y=1 and x = -10, is 1*(-10) > 0? No.
If y = 10 and x = 1, is 1*10 > 0? Yes.
Since the answer can be both No and Yes, insufficient.

Statements 1 and 2 combined:
Linking together the two statements, we get:
y-2 < x < 2y-6
y-2 < 2y-6
y > 4.
Since y > 4 and x > y-2, we know that x > 2.
Thus, x and y are both positive.
Sufficient.

The correct answer is C.

Thanx guru...awesome explaination.

I got different values for x and y, but both are positive. Would someone tell me where am I wrong?

Here's what I did:

x - y > -2
-x + 2y > 6 (Note: x - 2y < -6 mutiplied by -1)
y > 4

x - 2y < -6
-2x + 2y < 4 (Note: x - y > -2 multiplied by -2)
-x < -2 Thus x > 2

I got y > 4 and x > 2 are these values correct?

MAAJ wrote:I got different values for x and y, but both are positive. Would someone tell me where am I wrong?

Here's what I did:

x - y > -2
-x + 2y > 6 (Note: x - 2y < -6 mutiplied by -1)
y > 4

x - 2y < -6
-2x + 2y < 4 (Note: x - y > -2 multiplied by -2)
-x < -2 Thus x > 2

I got y > 4 and x > 2 are these values correct?

It looks as though you submitted your post as I was editing a typo in mine. We got the same results.

Oh thanks!

GMATGuruNY wrote:

tonebeeze wrote:Is XY > 0?

(1) X - Y > -2
(2) X - 2Y < -6

Statement 1: x > y-2
If y=2 and x= 1, is 1*2 > 0? Yes.
If y= -1 and x = 1, is 1*(-1) > 0? No.
Since the answer can both Yes and No, insufficient.

Statement 2: x < 2y-6
If y=1 and x = -10, is 1*(-10) > 0? No.
If y = 10 and x = 1, is 1*10 > 0? Yes.
Since the answer can be both No and Yes, insufficient.

Statements 1 and 2 combined:
Linking together the two statements, we get:
y-2 < x < 2y-6
y-2 < 2y-6
y > 4.
Since y > 4 and x > y-2, we know that x > 2.
Thus, x and y are both positive.
Sufficient.

The correct answer is C.

I did solve the question in similar manner. But is it okay to add Y and 2Y (read variables)in above equations even though we don't know their signs?

xyzx5230 wrote:I did solve the question in similar manner. But is it okay to add Y and 2Y (read variables)in above equations even though we don't know their signs?

Adding is always fine - your inequalities won't flip.

Subtracting is NOT necessarily fine, however - you have to recognize that subtract is like adding by a negative, so your inequality will flip.

For example:

x > y
2x > 3 - y

Adding these together, I get 3x > 3, or x > 1.

But let's say I wanted to subtract one from the other. Many people would do

(x > y)
- (2x > 3 - y)
----------------
-x > 2y - 3

But this is INCORRECT.

(x > y) - (2x > 3 - y) is really

(x > y) + -(2x > 3 - y), or

(x > y) + (-2x < y - 3), or

(x > y)
+ (y - 3 > -2x), or

x + y - 3 > y - 2x, or

x - 3 > -2x, or

3x > 3, or x > 1