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09 Dec 2025, 07:52
Kudos
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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
Number of students = 10
Average score of 10 students = 60
Total score of 10 students = 60*10 = 600
Average score of bottom 5 students = 55
Total score of bottom 5 students = 55*5 = 275
Total score of top 5 students = 600 - 275 = 325
To maximize the score of the topper, score of remaining 9 students need to be minimized.
Possible scores of bottom 5 students = {55,55,55,55,55}
Let the score of the topper be x.
Possible scores of top 5 students to maximise topper's score = {55,56,57,58,x}
55+56+57+58+x = 325
x = 99
The maximum possible score of the topper = 99
IMO C
If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is
Number of students = 10
Average score of 10 students = 60
Total score of 10 students = 60*10 = 600
Average score of bottom 5 students = 55
Total score of bottom 5 students = 55*5 = 275
Total score of top 5 students = 600 - 275 = 325
To maximize the score of the topper, score of remaining 9 students need to be minimized.
Possible scores of bottom 5 students = {55,55,55,55,55}
Let the score of the topper be x.
Possible scores of top 5 students to maximise topper's score = {55,56,57,58,x}
55+56+57+58+x = 325
x = 99
The maximum possible score of the topper = 99
IMO C
16 Dec 2025, 21:45
Kudos
Bookmarks
Average score of all 10 of em = 60
Total score of all 10 of em = 10 × 60 = 600
Average score of 5 low scorers = 60 - 5 = 55
Total score of 5 low scorers = 5 × 55 = 275
So.... total score of 5 top scorers = 600 - 275 = 325
Now.....da top 5 scorers must get distinct scores.....but one of their scores can be da same as a low scorer = 55 ..... because its not said that all 10 of em must get distinct scores.....only top 5 scorers must get distinct scores among them..... and because we wanna make da topper get maximum score.....we will make others get as low score as we can.....
lowest score da 5th guy among da 5 top scorers can get is = 55 ....[ any less and his score will be lower than a low scorer ]
....so da 4th guy among da top 5 scorers will get = 56 [ they must all get distinct scores ]
.....3rd guy will get = 57 .......2nd guy will get = 58 .......
5th, 4th, 3rd and 2nd guy will total get = 55 + 56 + 57 + 58 = 226
So.... their minimum total score is 226 ......
So.... da topper can maximum get = 325 - 226 = 99 ..........
!nah id win!
Total score of all 10 of em = 10 × 60 = 600
Average score of 5 low scorers = 60 - 5 = 55
Total score of 5 low scorers = 5 × 55 = 275
So.... total score of 5 top scorers = 600 - 275 = 325
Now.....da top 5 scorers must get distinct scores.....but one of their scores can be da same as a low scorer = 55 ..... because its not said that all 10 of em must get distinct scores.....only top 5 scorers must get distinct scores among them..... and because we wanna make da topper get maximum score.....we will make others get as low score as we can.....
lowest score da 5th guy among da 5 top scorers can get is = 55 ....[ any less and his score will be lower than a low scorer ]
....so da 4th guy among da top 5 scorers will get = 56 [ they must all get distinct scores ]
.....3rd guy will get = 57 .......2nd guy will get = 58 .......
5th, 4th, 3rd and 2nd guy will total get = 55 + 56 + 57 + 58 = 226
So.... their minimum total score is 226 ......
So.... da topper can maximum get = 325 - 226 = 99 ..........
!nah id win!
