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.