Since $a-b$ is even, this means
- both of them must be even or, ($a = 2n+k$ and $b=2n$ and where $k$ is even and $n$ might be even or odd so that $a-b=k$)
- both of them must be odd ($a=n$, and $b=n+k$ where $p$ is odd and $k$ is even so that $a-b=k$)
Case I: Both are even, say 4 and 6
A. $ab$ = 24
B. $a^2+b^2+1$ = 53
C. $a^2+b+1$ = 23
D. $ab−b$ = 18
Case II: Both are odd, say 3 and 7
Since options 2 and 3 are not true we will look at only options 1 and 4
A. $ab$ = 21
B. NA
C. NA
D. $ab−b$ = 14
So, $ab-b$, option $D$ is the answer.