XY can be even if at least one of the terms is Even

E x E = E

E X O = E

Statement 1)

5x - 4y = E

we can only get even when:

E - E or O - O

E-E

5x = even only when X is even

4y = is even no matter what Y is

0-0

5x = O ; x is ODD

4Y = O ; we have no solution for this

So, both 5x and 4y are EVEN and this statement is Sufficient

Statement 2)

6x+7Y = EVEN

either E+E or O+O

we know that 6X will always be E so

we need to check only

E+E

7Y = EVEN , so Y must be EVEN, so no matter what X is

XY = EVEN

Hence, D

What is OA ?

P.S. Maxx please post the OA with spoiler function

O - ODD
E- EVEN

RULES:

O*O = O
E*E = E
O*E = E

O+O = E
E+E = E
O-E = O

O-O=E
E-E = E
E-O = O

The product xy will be even if both x and y are even or either one of them is even from rules above

Stmt I

5x-4y is even

5x can be odd and 4y can be odd or 5x can be even and 4y can be even from the rules above for the difference to be even

However 4y cannot be odd since even or odd multiplied by even number 4 is even from the rules above. Therefore 4y is even (y can be odd) but for 5x to be even x has to be even (since 5 is odd if x were odd then odd*odd = odd but we want 5x to be even)

Since we have shown atleast x or y is even the product xy is always even

SUFF

Stmt II

6x+7y - > even

Similar to explanation above -- 6x has to be even (since 6 is even even*anyhting is even) where x xan be odd or even AND also 7y has to even and y has to be even for 7y to be even (since odd*odd will give you odd)

y has to be even therefroe xy is even whether x is even or odd

SUFF

D)