CAT (QA) PYQs

In an examination, the average marks of $4$ girls and $6$ boys is $24$. Each of the girls has the same marks while each of the boys has the same marks. If the marks of any girl is at most double the marks of any boy, but not less than the marks of any boy, then the number of possible distinct integer values of the total marks of $2$ girls and $6$ boys is

In a group of $10$ students, the mean of the lowest $9$ scores is $42$ while the mean of the highest $9$ scores is $47$. For the entire group of $10$ students, the maximum possible mean exceeds the minimum possible mean by

A CAT aspirant appears for a certain number of tests. His average score increases by $1$ if the first $10$ tests are not considered, and decreases by $1$ if the last $10$ tests are not considered. If his average scores for the first $10$ and the last $10$ tests are $20$ and 30, respectively, then the total number of tests taken by him is