Hi ceh232,
This question is based around a couple of Algebra patterns: Classic Quadratics.
We're told that 0 < X < Y, which means that we're dealing with positive numbers only. We're asked for the value of (X+Y)^2 / (X-Y)^2.
To start, we can rewrite the given question:
[X^2 + 2XY + Y^2] / [X^2 - 2XY + Y^2] = ?
By looking at the question in this way, we might find it easier to answer...
1) X^2 + Y^2 = 3XY
With this Fact, we can substitute in 3XY for "X^2 + Y^2" in the question...
[3XY + 2XY] / [3XY - 2XY]
Then we can combine "like terms" and simplify:
[5XY] / [XY] = 5/1 = 5. We now have the answer to the given question (and it's the ONLY answer).
Fact 1 is SUFFICIENT
2) XY = 3
With this fact, we can also substitute in a value, but we still don't know what X^2 or Y^2 actually equals. We end up with...
[X^2 + 2(3) + Y^2] / [X^2 - 2(3) + Y^2] = ?
Without those values, the answer to the question changes (TESTing X=1, Y=3 and X=1.5, Y=2 will give you two different results).
Fact 2 is INSUFFICIENT
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
