If n is an integer and if n^2 is a positive integer, which of the following must also be a positive integer?
(A) (n^2) + n
(B) (2 times (n^2)) minus n
(C) (n^2) minus (n^3)
(D) (n^3) + n
(E) (2 times (n^3)) + n
can you please explain this question. Thanks.

You know that n^2 is positive, but n can be negative. So start thinking of ways to eliminate choices.

A doesn’t have to be positive: if n = –1, then the expression equals zero.

B Will always be positive. There are no integer values for n that would make it negative or zero.

C will not be positive if n is positive. For example, 3^2 – 3^3 will be negative.

D will be negative if n is negative.

E will be negative if n is negative.

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