Answer: D

The most straightforward way for the expression to result in an integer is for both of the parts to be integers. First, simplify (n + 84)/n, which is equal to n/n + 84/n, or 1 + 84/n. The value of n has no effect on "1", so ignore that part. Now what we want to know is, for what value of n is 84/n - n/4 an integer?

In order that 84/n is an integer, n must be a factor of 84. There are many possibilities, including 1, 2, 42, and 84. In order than n/4 is an integer, n must be divisible by 4--a number such as 4, 8, 12, or 40.

We're looking, then, for the answer choice that fits both of those descriptions. 14 and 42 are factors of 84, but not divisible by 4. 16 and 24 are multiples of 4 but not factors of 84. That leaves only 28, which is divisible by 4 and a factor of 84. Thus, when n = 28, 84/n is an integer, and n/4 is an integer, meaning that 1 + 84/n - n/4 is an integer. Choice (D) is correct.