The mean of a set of 7 different positive integers
is 10. The median is 12. What is the maximum
possible value of the largest number?
(Source: Noetic Learning Challenge Math Online)
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Since the mean of the 7 numbers is 10, the sum of the 7 numbers is 7 × 10 = 70.
Since 12 is the median, 3 numbers must be less than 12, 1 number must equal 12
and 3 numbers must be greater than 12.
To find the maximum possible value of the largest number, we will choose
smallest possible numbers for all others.
 3 numbers that are less than 12: 1, 2, 3
 1 number is 12: 12
 3 numbers are greater than 12: 13, 14, *
The remaining number (the largest number) is: 70 – 1– 2– 3– 12– 13– 14 = 25.
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