imc

Let the sum of the scores of Isabella's first $6$ tests be $S$. Since the mean of her first $7$ scores is an integer, then $S+95\equiv 0\text{ (mod 7)}$, or $S\equiv 3\text{ (mod 7)}$. Also, $S\equiv 0\text{ (mod 6)}$, so by the CRT, $S\equiv 24\text{ (mod 42)}$. We also know that $91\cdot 6\le S\le 100\cdot 6$, so by inspection, $S=570$. However, we also have that the mean of the first $5$ test scores must be an integer, so the sum of the first $5$ test scores must be an multiple of $5$, which implies that the $6$th test score is $\boxed{100}$.