CAT (QA) PYQs

There are three persons $\mathrm{A}, \mathrm{B}$ and $C$ in a room. If a person $D$ joins the room, the average weight of the persons in the room reduces by $x$ kg . Instead of $D$ , if person $E$ joins the room, the average weight of the persons in the room increases by $2 \mathrm{x} \mathrm{kg}$. If the weight of $E$ is $12 \mathrm{~kg}$ more than that of $D$, then the value of $x$ is

In an examination, the average marks of $4$ girls and $6$ boys is $24$. Each of the girls has the same marks while each of the boys has the same marks. If the marks of any girl is at most double the marks of any boy, but not less than the marks of any boy, then the number of possible distinct integer values of the total marks of $2$ girls and $6$ boys is

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