Suppose that $a=\frac{1}{n}$, where $n$ is a positive integer with $n>1$.

Which of the following statements is true?
(A) $a<\frac{1}{a}<a^{2}$
(D) $\frac{1}{a}<a<a^{2}$
(B) $a^{2}<a<\frac{1}{a}$
(C) $a<a^{2}<\frac{1}{a}$
Since $a=\frac{1}{n}$ where $n$ is a positive integer with $n>1$, then $01$.

Thus, $0<a<1<\frac{1}{a}$, which eliminates choices (D) and (E).

Since $0<a<1$, then $a^{2}$ is positive and $a^{2}<a$, which eliminates choices (A) and (C).

Thus, $0<a^{2}<a<1<\frac{1}{a}$, which tells us that (B) must be correct.

ANswer: (B)