CAT (QA) PYQs

If $m$ and $n$ are integers such that $(m+2n)(2m+n) = 27$, then the maximum possible value of $2m-3n$ is

Let $N, x$ and $y$ be positive integers such that $N = x + y,$ $2 < x < 10$ and $14 < y < 23$. If $N > 25$, then how many distinct values are possible for $N?$

The number of pairs of integers ( $x, y$ ) satisfy $x \geq y \geq-20$ and $2 x+5 y=99$ is