Data Sufficiency

VJesus12 wrote:If x and y are positive integers, is y odd?

(1) (y+2)!/x! = odd
(2) (y+2)!/x! is greater than 2

The OA is C .

I am confuse here. Experts, may you give me some help? Thanks in advance.

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

Case 1: Say y = 1 (Odd) and x = 2, then (y+2)!/x! = (1+2)!/2! = 3!/2! = 1.2.3/1.2 = 3 (Odd).
Case 2: Say y = 2 (Even) and x = 4, then (y+2)!/x! = (2+2)!/4! = 4!/4! = 1 (Odd).

No unique answer. Insufficient

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

Case 1: Say y = 1 (Odd) and x = 2, then (y+2)!/x! = (1+2)!/2! = 3!/2! = 1.2.3/1.2 = 3 >2.
Case 2: Say y = 2 (Even) and x = 1, then (y+2)!/x! = (2+2)!/1! = 4!/1! = 1.2.3.4/1 = 12 >2.

No unique answer. Insufficient

(1) and (2) together

Case 2 of Statement is not a valid case as 1 is not greater than 2, while Case 2 of Statement 2 is also not valid as 12 is not odd.

When we have y odd and x - y = 1, the value of (y+2)!/x! would be odd and greater than 2. Sufficient.

Say y = 3 (Odd) and x = 4, then (y+2)!/x! = (3+2)!/4! = 5!/4! = 1.2.3.4.5/1.2.3.4 = 5 >2.

The correct answer: C

Hope this helps!

-Jay
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