CAT (QA) PYQs

The average of $30$ integers is $5$. Among these $30$ integers, there are exactly $20$ which do not exceed $5$. What is the highest possible value of the average of these $20$ integers?

A batsman played $n + 2$ innings and got out on all occasions. His average score in these $n + 2$ innings was 29 runs and he scored 38 and 15 runs in the last two innings. The batsman scored less than 38 runs in each of the first $n$ innings. In these $n$ innings, his average score was 30 runs and lowest score was $x$ runs. The smallest possible value of $x$ is

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