Carcass wrote:
The average (arithmetic mean) of x and x equals
(A) x if x > 0, and equals 0 if x ≤ 0
(B) -x if x < 0, and equals 0 if x ≥ 0
(C) 0, regardless of the value of x
(D) x, regardless of the value of x
(E) |x|, regardless of the value of x
Kudos for the right answer and explanation
Approach #1: Apply the average formula
Average \(= \frac{x + x}{2}= \frac{2x}{2}=x\)
Notice that x can be any value
Answer: D
Approach #2: Eliminate 4 answer choices
Try \(x = -1\)
Average \(= \frac{(-1) + (-1)}{2}= \frac{-2}{2}=-1\)
This means we can:
- eliminate answer choice A, since it says the average must equal 0 if x ≤ 0
- eliminate answer choice B, since it says the average must -(-1) (i.e., 1)
- eliminate answer choice C, since it says the average must equal 0
- eliminate answer choice D, since it says the average must equal |-1| (i.e., 1)
By the process of elimination, the correct answer must be D.
NOTE: I have change the correct answer to D
Cheers,
Brent