CAT (QA) PYQs

The arithmetic mean of scores of $25$ students in an examination is $50$. Five of these students top the examination with the same score. If the scores of the other students are distinct integers with the lowest being $30$, then the maximum possible score of the toppers 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

The average height of 22 toddlers increases by 2 inches when two of them leave this group. If the average height of these two toddlers is one-third the average height of the original 22, then the average height, in inches, of the remaining 20 toddlers is