Question

If 'x' and 'y' are positive integers and 'x + y' is even, then which of the following must always be even?

• A. x
• B. y
• C. x (y + 1)
• D. (x+1) (y + 1)

Answer 1

The Correct Option is C

Step 1: For x + y to be even, either both x and y are even, or both are odd.

• If both are even: x(y + 1) is even, as the product of an even number is always even.
• If both are odd: x(y + 1) is still even, as the product of an odd number and an even number is even.

Conclusion: Hence, x(y + 1) is always even.