CAT (QA) PYQs

Let $x, y, z$ be three positive real numbers in a geometric progression such that $x<y<z$. If $5 x, 16 y$, and $12 z$ are in an arithmetic progression then the common ratio of the geometric progression is

Let both the series $a_1, a_2, a_3, \dots$ and $b_1, b_2, b_3 \dots$ be in arithmetic progression such that the common differences of both the series are prime numbers. If $a_5 = b_9$, $a_{19} = b_{19}$ and $b_2 = 0$, then $a_{11}$ equals

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