Bunuel wrote:

If \(p\) and \(q\) are nonzero integers and \(n=\frac{p}{q}\), is \(n\) an integer?

(1) \(n^2\) is an integer.

(2) \(\frac{2n+4}{2}\) is an integer.

Good question. I was wondering why do we have n=P/Q with both p,q = non zero integers, but this information is useful to evaluate statement 1.

Per statement 1, \(n^2\) = integer. Now \(n^2=4\) or \(n^2 =2\) but \(n^2\)=not possible as this will give n = \(\sqrt{2}\) but as n=P/Q (ratio of integers), it can not be equal to \(\sqrt{2}\). For n = \(\sqrt{2}\) = \(\sqrt{2}/1\) ----> this means that P = \(\sqrt{2}\) and this will violate the information in the question that P is an integer. Thus this statement is sufficient.

Per statement 2, 2n+4 / 2 = integer ---> n+2 = integer ---> n = integer - 2 = another integer. Thus this statement is sufficient as well.

Thus D is the correct answer.