First notice that \(0 < k < k+1 < k+2\)
However, when we try to add the n to this inequality, we can't tell where it goes.
It COULD be the case that we have: \(0 < k < n < k+1 < k+2\)
OR
It COULD be the case that we have: \(0 < k < k+1 < n < k+2\)

This certainly suggests that the correct answer is D.
However, let's be sure and find some possible values to test.

case i: Since n is an integer, and k is not an integer and since \(0 < k < n < k + 2\), one possible pair of values is \(n=3\) and \(k=1.5\)
We get:
Quantity A: n = 3
Quantity B: k + 1 = 1.5 + 1 = 2.5
In this case, Quantity A is greater

case ii: Another possible pair of values is \(n=2\) and \(k=1.5\)
We get:
Quantity A: n = 2
Quantity B: k + 1 = 1.5 + 1 = 2.5
In this case, Quantity B is greater

Answer: D

Cheers.
Brent

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