CAT (QA) PYQs

Five students, including Amit, appear for an examination in which possible marks are integers between $0$ and 50, both inclusive. The average marks for all the students is $38$ and exactly three students got more than 32. If no two students got the same marks and Amit got the least marks among the five students, then the difference between the highest and lowest possible marks of Amit is

In an examination, the average marks of students in sections $A$ and $B$ are $32$ and $60$, respectively. The number of students in section $A$ is $10$ less than that in section $B$ . If the average marks of all the students across both the sections combined is an integer, then the difference between the maximum and minimum possible number of students in section $A$ is

The mean of all $4-$digit even natural numbers of the form $'aabb',$ where $a > 0,$ is