CAT (QA) PYQs

The value of the sum $7 \times 11 + 11 \times 15 + 15 \times 19 + \dots + 95 \times 99$ is

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

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