If a and b are both integers greater than 0 and the average (arithmeti

The average (arithmetic mean) of the values above is 3

So, we can write: \(\frac{1 + 4 + a + 5 + b + 4}{6} = 3\)

Multiply both sides of the equation by \(6\) to get: \(1 + 4 + a + 5 + b + 4 = 18\)

Simplify: to get: \(a + b + 14 = 18\)

Subtract \(14\) from both sides: \(a + b = 4\)

Since we're told \(a\) and \(b\) are POSITIVE integers, there are only two possible pairs of values for \(a\) and \(b\).
Let's examine each possible case....

Case i: The two numbers could be 1 and 3, in which case the six numbers (when displayed in ascending order) are {1, 1, 3, 4, 4, 5}
In this case, the median = 3.5
Since 3.5 does not appear among the answer choices, we'll check case ii

Case ii: The two numbers could be 2 and 2, in which case the six numbers (when displayed in ascending order) are {1, 2, 2, 4, 4, 5}
In this case, the median = 3

Answer: D

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