M7MBA wrote: ↑Wed Jun 24, 2020 6:40 am
\(\{3, k, 2, 8, m, 3\}\)
The arithmetic mean of the list of numbers above is \(4.\) If \(k\) and \(m\) are integers and \(k \ne m,\) what is the median of the list?
(A) 2
(B) 2.5
(C) 3
(D) 3.5
(E) 4
[spoiler]OA=C[/spoiler]
Source: Official Guide
Solution:
Using the average formula: average = sum/number, we see that the sum of these numbers is 24. Thus we have:
3 + k + 2 + 8 + m + 3 = 24
16 + k + m = 24
k + m = 8
Since k ≠ m and assuming that k < m, then the ordered pairs of (k, m) could be (3, 5), (2, 6), (1, 7), (0, 8), etc.
Let’s investigate the possible ordered pairs further:
If (k, m) = (3, 5), then the numbers in ascending order are:
2, 3, 3, 3, 5, 8 --- with median = 3
If (k, m) = (2, 6), then the numbers in ascending order are:
2, 2, 3, 3, 6, 8 --- with median = 3
If (k, m) = (1, 7), then the numbers in ascending order are:
1, 2, 3, 3, 7, 8 --- with median = 3
If (k, m) = (0, 8), then the numbers in ascending order are:
0, 2, 3, 3, 8, 8 --- with median = 3
At this point, we can see that no matter how we “stretch” k and m (e.g., let’s say (k, m) = (-92, 100)), we would still have median = 3.
Answer: C 
