CAT 2022 Question Paper (Slot 2) Question 65

Question 65

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

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.


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Comments
Harshit

3 months, 1 week ago

why can't the minimum score for amit be 0. for eg scores of amit, p2, p3, p4, p5 can be 0,7,60,61,62.
Here the average comes as 38, 3 persons score more than 32 and 2 persons score less than 32.
So Why can't amit be 0?

Prateek Jain

1 month, 4 weeks ago

The test itself is of 50 marks, so 60 can't be the score out of 50

cracku

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