abhasjha wrote:Is xy > 0?

(1) x - y > -2
(2) x - 2y > -6

Target question: Is xy > 0?

Statement 1: x - y > -2
Let's multiply both sides of the inequality by -1 to get: y - x < 2
This tells us that y is less than 2 greater than x.
Does this provide enough information to answer the target question? No.
Consider these two possible cases x and y that satisfy the given inequality:
Case a: x = 1, y = 1, in which case xy > 0
Case b: x = -1, y = 0.5, in which case xy < 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x - 2y > -6
Let's multiply both sides of the inequality by -1 to get: 2y - x < 6
This tells us that 2y is less than 6 greater than x.
Does this provide enough information to answer the target question? No.
Consider these two possible cases x and y that satisfy the given inequality:
Case a: x = 1, y = 1, in which case xy > 0
Case b: x = -1, y = 0.5, in which case xy < 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 says that y is less than 2 greater than x
Statement 2 says that 2y is less than 6 greater than x
Since both conclusions are very similar, and since each statement alone was INSUFFICIENT, I suspect that the combined statements are not sufficient, so I'll start looking for some values that prove insufficiency.
Here are two sets of values:
Case a: x = 1, y = 1, in which case xy > 0
Case b: x = -1, y = 0.5, in which case xy < 0
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

Uva@90 wrote:

Brent@GMATPrepNow wrote:

abhasjha wrote:Is xy > 0?

(1) x - y > -2
(2) x - 2y > -6

Target question: Is xy > 0?

Statement 1: x - y > -2
Let's multiply both sides of the inequality by -1 to get: y - x > 2
This tells us that y is more than 2 greater than x.
Does this provide enough information to answer the target question? No.
Consider these two possible cases x and y that satisfy the given inequality:
Case a: x = 1, y = 4, in which case xy > 0
Case b: x = -1, y = 5, in which case xy < 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x - 2y > -6
Let's multiply both sides of the inequality by -1 to get: 2y - x > 6
This tells us that 2y is more than 6 greater than x.
Does this provide enough information to answer the target question? No.
Consider these two possible cases x and y that satisfy the given inequality:
Case a: x = 1, y = 4, in which case xy > 0
Case b: x = -1, y = 5, in which case xy < 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 says that y is more than 2 greater than x
Statement 2 says that 2y is more than 6 greater than x
Since both conclusions are very similar, and since each statement alone was INSUFFICIENT, I suspect that the combined statements are not sufficient, so I'll start looking for some values that prove insufficiency.
Here are two sets of values:
Case a: x = 1, y = 4, in which case xy > 0
Case b: x = -1, y = 5, in which case xy < 0
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

Brent,
If we Multiply both side of the Inequality by same negative number we have to change direction of inequality na ?
Am I right ?

Let's multiply both sides of the inequality by -1 to get: y - x > 2

Regards,
Uva.

Ooops!
Thanks for catching that, Uva.
I edited my response accordingly.

Cheers,
Brent

TJerry wrote:Why we multiply both side of the Inequality by same negative number we have to change direction of inequality? Please help!

My blog is looking for clever experts.

Multiplying both sides by -1 wasn't entirely necessary. I just used that to get a better idea sense of the relationship between x and y.

With the given inequality, x - y > -2, it's hard to tell what's going on. For example, what does it mean if we say that x - y = -1? It means that y is 1 greater than x, but that might not be readily obvious to everyone.

If we multiply both sides by -1, we get y - x < 2
So, for example, if y - x = 1, I know that y is 1 greater than x
If y - x = 0.5, I know that y is 0.5 greater than x
If y - x = 0, I know that y is equal to x
In general, I can conclude that y is less than 2 greater than x.

Cheers,
Brent