CAT (QA) PYQs

If certain amount of money is divided equally among n person, each one receives Rs $352$. However, if two persons receive Rs $506$ each and the remaining amount is divided equally among the other persons, each of them received less than or equal to Rs $330$. Then, the maximum possible value of $n$ is

For some constant real numbers $p, k$ and $a$ consider the following system of linear equations in $x$ and $y$:

$px - 4y = 2$

$3x + ky = a$

A necessary condition for the system to have no solution for $(x, y)$ is

For some real numbers $a$ and $b$, the system of equations $x + y = 4$ and $(a + 5)x + (b^2 - 15)y = 8b$ has infinitely many solutions for $x$ and $y$. Then, the maximum possible value of $ab$ is