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Question

The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is

CAT 2021

A
99
CORRECT ANSWER WRONG ANSWER
B
100
CORRECT ANSWERWRONG ANSWER
C
87
CORRECT ANSWER WRONG ANSWER
D
95
CORRECT ANSWER WRONG ANSWER
Solution

Correct option is

(A)

Explanatory Answer :

Total marks of (all 10) = 600

Total of (bottom 5) = 55x5 => 275

We have given, Top 5 = 600-275 => 325

 

ATQ

Each of the top scorer had distinct integral scorer

Let, a < b < c < d < e (Where e is max. score)

and we know

a + b + c + d + e = 325

a,b,c,d has to be minimum and, all five bottom score = 55

So, We have lowest value 55 and sum of top 5 were 325 where e is max.

 

325 = 55 + 56 + 57 + 58 + e

e = 99

 

Hence, the answer is 99