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

A lab experiment measures the number of organisms at $8$ am every day. Starting with $2$ organisms on the first day, the number of organisms on any day is equal to $3$ more than twice the number on the previous day. If the number of organisms on nth day exceeds one million, then the lowest possible value of $n$ is

Consider the sequence $t_1 = 1$, $t_2 = -1$ and $t_n = \left(\frac{n-3}{n-1}\right) t_{n-2}$ for $n \ge 3$. The, the value of the sum $\frac{1}{t_2} + \frac{1}{t_4} + \frac{1}{t_6} + \dots + \frac{1}{t_{2022}} + \frac{1}{t_{2024}}$ is