CAT (QA) PYQs

An elevator has a weight limit of $630$ kg. It is carrying a group of people of whom the heaviest weighs $57$ kg and the lightest weighs $53$ kg. What is the maximum possible number of people in the group?

For natural numbers $x$, $y$, and $z$, if $xy + yz = 19$ and $yz + xz = 51$, then the minimum possible value of $xyz$ is

Let $f(x) =$ min{$2x², 52-5x$}, where x is any positive real number. Then the maximum possible value of $f(x)$ is