IPMAT Indore 2025 (SA) PYQs

If $|x| <100$ and $|y| <100$, then the number of integer solutions of $(x, y)$ satisfying the equation $4x + 7y = 3$ is

Let $[x]$ denote the greatest integer not exceeding $x$ and {$x$} $= x - [x]$ If $n$ is a natural number, then the sum of all values of $x$ satisfying the equation $2[x] = x + n${$x$} is