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?

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

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