CAT (QA) PYQs

Three positive integers $x, y$ and $z$ are in arithmetic progression. If $y − x > 2$ and $xyz = 5(x + y + z)$, then $z − x$ equals

If $\mathrm{x}_{0}=1, \mathrm{x}_{1}=2$, and $\mathrm{x}_{\mathrm{n}+2}=\frac{1+x_{n+1}}{x_{n}}, n=0,1,2,3 \ldots \ldots$., then $x_{2021}$ is

Let $a_n$ and $b_n$ be two sequences such that $a_n = 13 + 6 (n - 1)$ and $b_n = 15 + 7 (n - 1)$ for all natural numbers $n$. Then, the largest three digit integer that is common to both these sequences, is