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, 2023

Algebra Difficulty 2.5 Junior Find the answer Canada

Suppose that $a =
$\dfrac{1}{n}$ $, where$ n$ is a
positive integer with $n > 1$ .
Which of the following statements is true?

Pick one

Solution

Since $a = \dfrac{1}{n}$ where
$n$ is a positive integer with $n > 1$ , then $0 < a < 1$ and $\dfrac{1}{a} = n > 1$ .

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

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.