For real numbers $a, b$ and $c$,
$$a > a \cdot b > 2 \cdot a > a \cdot c$$
is known to hold.
Accordingly, which of the following could be the representation of the numbers $\mathbf{a, b}$ and $\mathbf{c}$ on the number line?
A) [number line A] B) [number line B] C) [number line C] D) [number line D] E) [number line E]

Let $x$ and $y$ be real numbers,
$$x^{2} \cdot y^{2} < x \cdot y < x^{2} \cdot y$$
Given this inequality.
Accordingly,
I. $x < 1$ II. $y < 1$ III. $x \cdot y < 1$
Which of these statements are true?
A) Only I B) Only II C) I and III D) II and III E) I, II and III

Let $x$ be a real number different from $-1, 0$ and $1$.
$$\left\{ x^{3}, x^{2}, x, -x, -\frac{1}{x} \right\}$$
When the elements of the set are arranged from smallest to largest, which element never occupies the exact middle position?
A) $x^{3}$ B) $x^{2}$ C) $x$ D) $-x$ E) $-\frac{1}{x}$