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08 Jul 2025, 19:55
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It is given that median is 27 for the 7 nos. we have to determine minimum possible value of maximum no
4th no =27
now to minimize 7th no, we have to maximize all other nos
24,25,26,27 will minimize other values, their sum = 102
Now arithmetic mean= 30
total sum = 210
sum of remaining 3 nos. = 210-102=108
we have to maximize 5th & 6th no solving gives only one sol
35,36,37= 108
So the answer is 37 which is option D.
4th no =27
now to minimize 7th no, we have to maximize all other nos
24,25,26,27 will minimize other values, their sum = 102
Now arithmetic mean= 30
total sum = 210
sum of remaining 3 nos. = 210-102=108
we have to maximize 5th & 6th no solving gives only one sol
35,36,37= 108
So the answer is 37 which is option D.
08 Jul 2025, 20:02
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mean = 30
sum of all scores = 30*7 = 210
we have 7 students, with median being 27: _ , _ , _ , 27, _ , _ ,H
for the highest score H to be minimum, we need to maximise all other scores
For the 3 lowest scores, maximum value can be 27, and for the 5th and 6th score, maximum value can be the highest score.
27, 27 , 27 , 27, H , H,H
>> 4*27 + 3H = 210
>> 3H = 102
>> H = 34
So, the minimum possible H, when all others are maximized is 34.
Answer is A
sum of all scores = 30*7 = 210
we have 7 students, with median being 27: _ , _ , _ , 27, _ , _ ,H
for the highest score H to be minimum, we need to maximise all other scores
For the 3 lowest scores, maximum value can be 27, and for the 5th and 6th score, maximum value can be the highest score.
27, 27 , 27 , 27, H , H,H
>> 4*27 + 3H = 210
>> 3H = 102
>> H = 34
So, the minimum possible H, when all others are maximized is 34.
Answer is A
08 Jul 2025, 20:43
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we have 7 scores of which the median score is 27:
_ _ _ 27 _ _ _
to find the smallest possible maximum score, all the values before median will be same as median so that they can get closest to the mean score of 30:
27 27 27 27 _ _ _
since the mean is 30, the four 27s have created a deficit of 4 x (30-27) = 12.
so the remaining 3 values must create a surplus of 12 to get to the mean of 30.
the next 3 values must be 12/3 = 4 more than 30 to create the surplus, that is 34
27 27 27 27 34 34 34
Answer is 34
_ _ _ 27 _ _ _
to find the smallest possible maximum score, all the values before median will be same as median so that they can get closest to the mean score of 30:
27 27 27 27 _ _ _
since the mean is 30, the four 27s have created a deficit of 4 x (30-27) = 12.
so the remaining 3 values must create a surplus of 12 to get to the mean of 30.
the next 3 values must be 12/3 = 4 more than 30 to create the surplus, that is 34
27 27 27 27 34 34 34
Answer is 34
