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

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

Ramesh and Gautam are among $22$ students who write an examination. Ramesh scores $82.5$. The average score of the $21$ students other than Gautam is $62$. The average score of all the $22$ students is one more than the average score of the $21$ students other than Ramesh. The score of Gautam is