CAT 2022 Slot 2 QA Question & Solution
Question
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
Options
Solution
The average marks for all the students is 38.
Sum = 5*38 = 190
To find the minimum marks scored by Amit, we need to maximise the score of remaining students.
Maximum scores sum of remaining students = 50 + 49 + 48 + 32 = 179
Minimum possible score of Amit = 190 - 179 = 11
It is given, Amit scored least. This implies maximum possible score of Amit is 31.
Difference = 31 - 11 = 20
The answer is option D.