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Question

Positive integers from 1 to 45, are placed in 5 groups of 9 each. Then highest possible average of the medians of these 5 groups is

A
31
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B
33
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C
29
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D
27
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Solution

The correct option is A 31
Dividing the numbers into sets of 9.
Median is the middle number when 9 numbers are arranged in ascending or descending order.
Median is the 5th number and we will have 4 numbers that are greater than the 5th number and remaining 4 numbers should be as small as possible because they are not contributing to increase median.
Largest possible median is 41
So, possible set representation would be {1,2,3,4,41,42,43,44,45},{5,6,7,8,36,37,38,39,40},{9,10,11,12,31,32,33,34,35},{13,14,15,16,26,27,28,29,30},{17,18,19,20,21,22,23,24,25}
Corresponding median of above sets are 41,37,31,26,21
Now, mean of these medians is
21+26+31+36+415=1555=31

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