sachin_yadav wrote:Is xy > 0 ?
(1) x - y > -2
(2) x - 2y < -6

OA is C

[spoiler]It took me 2 mins 47 secs. My first approach was using numbers of different signs and then solving two simultaneous equations in the end. Is there any other faster approach ?

[/spoiler]

Would this be faster? It might be or it might be a source of ideas anyway.

First check Statement 1 by adding y to both sides to create x > y - 2. So if y >= 2, they are both positive. If y < 2, x could be positive, negative or 0. So Statement 1 is insufficient.

Statement 2 similarly becomes x < 2y - 6. If y > 3, then x could be positive, negative or 0. Insufficient.

Then look at the two equations and notice that we can make their left sides the same by adding y to both sides of Statement 2 to get x - y < y - 6.

We can then combine this with Statement 1 to get y - 6 > x - y > -2 So y - 6 > -2 and y > 4.

Substitute 4 into Statement 1 and get x - 4 > -2. x > 2. For any higher y, x is still positive. So all x and all y are positive and xy > 0.

Choose C.

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 is YES in the first case but NO in the second case, 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 is NO in the first case but YES in the second case, INSUFFICIENT.

Statements 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, with the result that xy > 0.
SUFFICIENT.

The correct answer is C.

I expressed both inequalities in terms of lines.

i.e. From (1),

x - y > -2
x > y - 2
y < x + 2

Charting the line, you will see that this inequality is satisfied in all four cartesian quadrants:

Quadrant I: x is +ve, y is +ve
Quadrant II: x is -ve, y is +ve
Quadrant III: x is -ve, y is -ve
Quadrant IV: x is +ve, y is -ve

Thus, (1) is insufficient. Scratch answers A and D.

From (2),

x - 2y < -6
2y - 6 > x
2y > x + 6
y > x/2 + 3

Charting the line, you will see that this inequality is satisfied in three quadrants:

Quadrant I: x is +ve, y is +ve
Quadrant II: x is -ve, y is +ve
Quadrant III: x is -ve, y is -ve

Therefore, (2) is insufficient, scratch answer B.

Combining both charted lines. You will see that the only area that satisfies both inequalities is in Quadrant I, hence both x and y are both +ve, meaning xy > 0 always.

*Note: for xy > 0, x and y must both be in either the first quadrant (where both are positive), or the third quadrant (where both are negative).

Answer is C. 100 seconds.

Here's one more spiffy way to evaluate the two statements.

Once we've eliminated S1 and S2 alone, we can write the two inequalities as

x > y - 2
2y - 6 > x

Combining the two inequalities, we get 2y - 6 > x > y - 2. Since 2y - 6 > y - 2, we find y > 4. Since x > y - 2, we know x > 4 - 2, or x > 2. So they're both positive, and we're set!

[email protected] wrote:Hi sachin_yadav,

This DS question is perfect for TESTing VALUES.

We're asked if XY > 0? This is a YES/NO question.

Fact 1: X - Y > - 2

This can rewritten as:

X + 2 > Y

If X = 1, Y = 1, XY = 1 and the answer to the question is YES
If X = 1, Y = 0, XY = 0 and the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: X - 2Y < -6

This can be rewritten as:

X + 6 < 2Y

If X = 0, Y = 4, then XY = 0 and the answer to the question is NO
If X = 1, Y = 4, then XY = 4 and the answer to the question is YES
Fact 2 is INSUFFICIENT

Combined, we know:
X + 2 > Y
X + 6 < 2Y

2Y - 6 > X > Y - 2

From this, with a bit of "tinkering", we can deduce that...

Y CANNOT be 0, since -6 > X > -2 is impossible
Y CANNOT be negative (it would create the same "impossible" situation)

Since 2Y - 6 > Y - 2
2Y - Y > -2 + 6

Y MUST be > 4

Since Y > 4...

X - 2 > 4

X MUST be > 2

This means that X and Y are BOTH POSITIVE, so the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

Hi Rich,

Please review the highlighted part in red as it must be 'x+2>4'NOT 'x-2>4'.

Thanks

I think that was already super fast! I attempted this question in 4 mins

sachin_yadav wrote:Is xy > 0 ?
(1) x - y > -2
(2) x - 2y < -6

OA is C

We need to determine whether the product of x and y is positive. We should recall that the product of two numbers is positive only if both the numbers are positive or if both are negative.

Statement One Alone:

x - y > -2

Statement one tells us that the difference between x and y is -2; it does not tell us anything about the signs of x and y. For instance, if x = 2 and y = 1, we have x - y = 1 > -2, and xy is positive. However, if x = 3 and y = -2, 3 - (-2) = 5 > -2, but xy is negative. Statement one alone is not sufficient. We can eliminate answer choices A and D.

Statement Two Alone:

x - 2y < -6

Again, we have a statement that tells us nothing about the signs of x and y. For instance, if x = 3 and y = 5, then x - 2y = 3 - 2(5) = 3 - 10 = -7 < -6, and xy is positive. However, if x = -1 and y = 5, then x - 2y = -1 - 2(5) = -11 < -6, and xy is negative. Statement two alone is not sufficient. We can eliminate answer choice B.

Statements One and Two Together:

Let's manipulate the first inequality to read: y < x + 2. Similarly, we can manipulate the second inequality to read: y > (1/2)x + 3.

Thus, we can say the following:

(1/2)x + 3 < y < x + 2

(1/2)x + 3 < x + 2

x + 6 < 2x + 4

2 < x

Thus, x is positive.

We also know the following:

y > (1/2)x + 3

Since x is greater than two, let's see what we can determine about y, if we substitute 2 for x.

y > (1/2)(2) + 3

y > 4

So y is positive as well. Both statements together are sufficient.

Answer: C