IPMAT Indore 2019 (SA) PYQs

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

If $m$ and $n$ are two positive integers such that $7m + 11n = 200$, then the minimum possible value of $m + n$ is