selango wrote:Set S contains seven distinct integers. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ?
A. m
B. 10m/7
C. 10m/7 - 9/7
D.5m/7 + 3/7
E.5m
OA C
Since there's a variable in the answer choices, we can plug in.
Plug in m=5.
For the median to be 5, we need to choose 3 distinct integers that are smaller than 5 and 3 distinct integers that are larger than 5. Since we're trying to maximize the average, we want each integer to be as large as possible.
The largest allowed value is 2m = 2*5 = 10. So the 3 larger integers will have to be 8, 9, 10.
For the 3 distinct integers smaller than 5, the largest possible are 2, 3, 4.
So our 7 integers are 2, 3, 4, 5, 8, 9, 10.
The average = (2 + 3 + 4 + 5 + 8 + 9 + 10)/7 = 41/7.
Only answer choice C works: 10m/7 - 9/7 = 10*5/7 - 9/7 = 50/7 - 9/7 = 41/7.
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