(1)
5x - 4y = 2k
5x = 2(k + 2y)

this means 5x is even, which in turn means x is even. If x is even, it would mean xy is even

Sufficient

(2)
6x + 7y = 2k
7y = 2(k - 3x)

7y is even, which in turn means y is even, and if so, xy ought to be even

Sufficient

So, either statement is sufficient, i.e. (D)

OA please?

If x and y are positive integers, is the product xy even?

(1) 5x - 4y is even => (5x - Even) is Even => 5x is Even => x is Even => xy is Even - Sufficient

(2) 6x + 7y is even => (7y + Even) is Even => 7y is Even => y is Even => xy is Even - Sufficient

IMO Option D

Concept recap :
Even+Even = Even
Even*Even = Even
Even* Odd = Even

Statement 1. 5x - 4y is even i.e. 5x - 4y = 2k
Difference of two numbers is even if either both of them are odd or both of them are even.
Here, 4y is always even. So, 5x is also even.
Since 5x is even, we can say that x is even.
Now, xy will be even because the product of an even no with any positive integer is always even. Hence, Sufficient.
Statement 2. 6x + 7y is even.
6x is eve n because it is divisible by 2. So, 7y has to be even.
For 7y to be even, y has to be even.
We know the product of an even no with a positive integer is even.
Hence, xy is even. Hence, Sufficient.