Consider a set of 11 distinct positive integers whose average is 20. If the average of the initial six integers in this set is 14, and the average of the final six integers is 24, determine the value of the sixth integer in the set.
Sum of 11 numbers = 11 X 20 = 220 Sum of first 6 numbers = 6 X 14 = 84 Sum of last 6 numbers = 6 X 24 = 144 Sixth number = 144 + 84 - 220 = 8
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