Bunuel wrote:

If j is an integer, is k an integer?

(1) The average (arithmetic mean) of 1, 2k, and k – 4 is j.

(2) The average (arithmetic mean) of j and k is not an integer.

(1) Given that (1 + 2k + k-4)/3 = j. OR 3k-3 = 3j

Or 3k = 3j+3 Or k = j+1 (dividing both sides by 3).

Now since j is an integer, j+1 will also be an integer. Hence k is an integer.

Sufficient.

(2) (j+k)/2 is not an integer, so j+k is not divisible by 2. But given that j is an integer.

We can have two cases:

k could be an integer but such that sum j+k is odd (eg, we can have j odd and k even, say j=3, k=4).

Or

k might not be an integer, in which case addition with j will be non-integer, thus anyway not divisible by 2 (say j=3, k=4.5)

So k might or might not be an integer.

Not Sufficient.

Hence

A answer