CAT (QA) PYQs

The average of three distinct real numbers is 28. If the smallest number is increased by 7 and the largest number is reduced by 10, the order of the numbers remains unchanged, and the new arithmetic mean becomes 2 more than the middle number, while the difference between the largest and the smallest numbers becomes 64. Then, the largest number in the original set of three numbers is

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?

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