Question 1118645: a set of six different positive integers has a median and mean of 6. if the largest number in the set is 12, what is the largest possible sum for the largest 3 numbers
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
(1) If a set of 6 different positive integers has a median of 6, then the average of the 3rd and 4th numbers must be 6.
(2) We want the sum of the last three numbers to be as large as possible; that means the sum of the first three integers must be as small as possible.
So try 1, 2, 3 for the first three numbers. That means the 4th integer is 9; the first 4 numbers are now 1, 2, 3, 9.
Can we find two more numbers that satisfy all the conditions of the problem? The sum of all six integers must be 36; and the last two numbers must be larger than 9. The sum of the first four integers is 15; the sum of the last two must be 21.
AHA! 10 and 11 work perfectly!
The numbers we want are 1, 2, 3, 9, 10, 11.
To answer the specific question that was asked, the sum of the largest three integers is 9+10+11 = 30.
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