The arithmetic mean of 9 distinct integers is 87 If none of the numbers is more than 100 and the ave...........

Quantitative Aptitude (CDS) Statistics

The arithmetic mean of 9 distinct integers is 87. If none of the numbers is more than 100 and the average of the smallest five numbers is 78, find the minimum value of the sixth number.

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Explanation:

If the average of 9 numbers is 87, then the sum of these 9 distinct numbers will be 9 X 87 = 783
Let the numbers be a1, a2, a3, …..a9 where a9> a8> …a1.
So, a1+a2+a3+a4+a5 = 78 X 5 = 390
Smallest value of a5 can be 80 when a1, a2, a3, a4, and a5 are 76, 77, 78, 79, 80.
This means that a6 > 80.
Now, the sum of the rest of the four numbers is 738-390 = 393
For a6 to be min, a7, a8, a9 must be max.
=> a6 + 98 + 99 + 100 = 393 or a6 = 96.
Thus, 96 is the correct answer