Hi Mechmeera,
This DS question hides a subtle pattern, but can be solved by TESTing VALUES and a bit of arithmetic.
We're asked if XY > 24. This is a YES/NO question.
1) Y - 2 < X
From this Fact, we know that Y < X + 2
IF...
X = 1
Y = 0
(1)(0) is NOT greater than 24 and the answer to the question is NO.
IF...
X = 10
Y = 3
(10)(3) IS greater than 24 and the answer to the question is YES.
Fact 1 is INSUFFICIENT
2) 2Y > X + 8
IF...
X = 0
Y = 9
(0)(9) is NOT greater than 24 and the answer to the question is NO.
IF...
X = 10
Y = 10
(10)(10) IS greater than 24 and the answer to the question is YES.
Fact 2 is INSUFFICIENT
Combined, we know...
Y < X + 2
2Y > X + 8
With these two inequalities, we can 'order' the pieces and make some deductions about the values of X and Y.
Since.... X + 8 > X + 2.......
2Y > X + 8 > X + 2 > Y
For 2Y to be greater than Y, Y must be POSITIVE.
Since X + 8 is greater than X + 2 by AT LEAST 6, the difference between 2Y and Y has to be greater than 6. This means that Y > 6.
By extension, since Y > 6...
X + 2 must ALSO be greater than 6, so X must be greater than 4.
Since X > 4 and Y > 6....XY will ALWAYS be greater than 24 and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
