CAT (QA) PYQs

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 distinct pairs of integers $(x, y)$ satisfying the inequalities $x > y \geq 3$ and $x + y < 14$ is

Suppose $a,b,c$ are three distinct natural numbers, such that $3ac = 8(a+b)$. Then, the smallest possible value of $3a+2b+c$ is