CAT (QA) PYQs

A CAT aspirant appears for a certain number of tests. His average score increases by $1$ if the first $10$ tests are not considered, and decreases by $1$ if the last $10$ tests are not considered. If his average scores for the first $10$ and the last $10$ tests are $20$ and 30, respectively, then the total number of tests taken by him is

Suppose hospital $A$ admitted $21$ less Covid infected patients than hospital $B$, and all eventually recovered. The sum of recovery days for patients in hospitals $A$ and $B$ were $200$ and $152$, respectively. If the average recovery days for patients admitted in hospital $A$ was $3$ more than the average in hospital $B$ then the number admitted in hospital $A$ was

The arithmetic mean of $x, y$ and $z$ is $80$, and that of $x, y, z, u$ and $v$ is $75$, where $u=(x+y) / 2$ and $v=(y+z) / 2$. If $x \geq z$, then the minimum possible value of $x$ is