IPMAT Indore (SA) PYQs

Suppose $a, b$ and $c$ are three real numbers such that Max$(a, b, c) \ +$ Min$(a, b, c) = 15$, and Median$(a, b, c) \ -$ Mean$(a, b, c) = 2.$ Then the median of $a, b$ and $c$ is

Let 50 distinct positive integers be chosen such that the highest among them is 100, and the average of the largest 25 integers among them exceeds the average of the remaining integers by 50. Then the maximum possible value of the sum of all the 50 integers is _________.

The average marks of $6$ students in a test is $64$. All the students got different marks, one of the students obtained $70$ marks and all other students scored $40$ or above. The maximum possible difference between the second highest and the second lowest marks is