Solution:

Before moving to the options, I listed two probabilities in which the number are either odd/even.

j=3; k=9 .:\(\frac{ 9}{9}\)= 1 i.e.\( \frac{odd}{odd}\)=odd

j=10; k=100 .:\( \frac{100}{100}\)= 1 i.e.\( \frac{even}{even}\)=odd

(A) j and k are both even- Possible (Case 2)- Incorrect

(B) j = k- Possible- Incorrect

(C) If j is even, k is even- Correct- The option choice says if, indicating possibility and this is one of the possibility we referred in the above example

(D) j is divisible by k- Incorrect- If I take j=3 and k=1. This can be a possible solution.

(E) j^2>k- Similar to D taking j=3 and k=1 we get can get this to be one of our possibility.- Incorrect

Hope this helps!