Data Sufficiency

Hi sana.noor,

While this is a crazy "looking" DS question, you can beat it by TESTing simple Values and/or using Number Properties:

We're told that X and Y are positive integers. We're asked if Y is odd? This is a YES/NO question.

Since this question deals with factorials, I'm going to write down the first few for easy reference:
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120

Fact 1: (Y+2)!/X! = ODD

Since the simplest odd number is 1, let's TEST Values:
X = 3
Y = 1
The answer to the question is YES

X = 4
Y = 2
The answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: (Y+2)!/X! > 2

Since > 2 does NOT necessarily mean an integer, we have lots of options to TEST Values:
X = 1
Y = 1
The answer to the question is YES

X=1
Y=2
The answer to the question is NO
Fact 2 is INSUFFICIENT

Combined, we know that (Y+2)! is EVEN. For (Y+2)!/X! = ODD, we'd have...
Even/? = ODD

This means that the denominator must be EVEN and for (Y+2)!/X! = ODD INTEGER > 2
Since we're dealing with factorials, this will only happen under certain conditions (not all) when the numerator is 1 more than the denominator.
X = 2, Y = 1 and the answer is YES
X = 4, Y = 5 and the answer is YES
X = 6, Y = 7 and the answer is YES

Combined, SUFFICIENT

Final Answer: C

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