CAT (QA) PYQs

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

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

How many different pairs $(a, b)$ of positive integers are there such that $a ≤ b$ and $\frac{1}{a} + \frac{1}{b} = \frac{1}{9}$