CAT (QA) PYQs

In a football tournament, a player has played a certain number of matches and $10$ more matches are to be played. If he scores a total of one goal over the next $10$ matches, his overall average will be $0.15$ goals per match. On the other hand, if he scores a total of two goals over the next $10$ matches, his overall average will be $0.2$ goals per match. The number of matches he has played is

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