This is a great Question.

Testing our knowledge on factorial theory.

So we are given that both x and y are integers

And we need to get whether or not y is odd

Lets see

Statement 1

(y+2)!/x! => odd

99!/99!=> 1 => odd => y is odd

98!/98!=1=> odd=> y is even

Hence using test cases we can say that this statement is insufficient.

Lets look at statement 2

(y+2)!/x! is greater than 2

hmm

101!/2! is greater than 2=> y is 99 which is odd

100!/2! is also greater than 2=> y is 98 which is even

Hence insufficient

Combing the two statements

(y+2)!/x! to be a odd number >2

101!/100!=> y=99=> odd

100!/99!=> notes this is not odd

Hmm

Intersting

Here we know that every other number in the factorial series is even number.

so if y will be even then y+2 will be even too and no matter what value of x we take => (y+2)!/x! will always be even (constraints two the combining the two statements)

Hence y must be odd

Hence C

This Solution is pretty messed up for my liking.

I think Using test cases really helps in this one. Doesn't it

_________________

Mock Test -1 (Integer Properties Basic Quiz) ---> http://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1676182

Mock Test -2 (Integer Properties Advanced Quiz) --->http://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1765951

Give me a hell yeah ...!!!!!