Hi All,

We're asked for the value of 2X/3Y. This question can be solved by TESTing VALUES.

1) (X^2)/(Y^2) = 36/25

IF....
X=6, Y=5, then the answer to the question is 12/15 = 4/5
X=6, Y= -5, then the answer to the question is 12/-15 = -4/5
Fact 1 is INSUFFICIENT

2) X^5/Y^5 > 1

With this inequality, we know that X and Y must be the SAME sign (either both positive or both negative).

IF....
X=6, Y=5, then the answer to the question is 12/15 = 4/5
X=6, Y=1, then the answer to the question is 12/3 = 4
Fact 2 is INSUFFICIENT

Combined, we know...
(X^2)/(Y^2) = 36/25
X^5/Y^5 > 1

Since X and Y must be the SAME sign, we have two immediate examples that 'fit' both Facts....
IF....
X=6, Y=5, then the answer to the question is 12/15 = 4/5
X= -6, Y= -5, then the answer to the question is -12/-15 = 4/5

X and Y could be other values though, but the only pairs of values that fit the first equation will be in the ratio of 6:5. For example....
IF....
X=12, Y=10, then the answer to the question is 24/30 = 4/5
X= -12, Y= -10, then the answer to the question is -24/-30 = 4/5
The answer will ALWAYS be 4/5.
Combined, SUFFICIENT

Final Answer: C

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