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# SAT Inequalities

If $$x<10<\frac{1}{x},$$ which of the following is a possible value for $$x$$?

(A) $$\ \ 9$$

(B) $$\ \ 8$$

(C) $$\ \ \frac{1}{8}$$

(D) $$\ \ \frac{1}{9}$$

(E) $$\ \ \frac{1}{11}$$

$-2x+4 > 28$

In the above inequality, which of the following values CANNOT be the value of $$x$$?

(A) $$\ \ -16$$
(B) $$\ \ -15$$
(C) $$\ \ -14$$
(D) $$\ \ -13$$
(E) $$\ \ -12$$

If $$x^{12}y^{7}z>0$$, which of the following must be true?

$$\begin{array}{r r c c r} &\text{I.} &xy&>0\\ &\text{II.} &xz&>0\\ &\text{III.} &yz&>0\\ \end{array}$$

(A) None
(B) I only
(C) II only
(D) III only
(E) II and III only

Let $$0 \leq m \leq 5$$ and $$-6 \leq n \leq 7$$. Which of the following represents all possible values of $$mn$$?

(A) $$\ \ mn = 5$$
(B) $$\ \ 0 \leq mn \leq 35$$
(C) $$\ \ -6 \leq mn \leq 35$$
(D) $$\ \ -30 \leq mn \leq 7$$
(E) $$\ \ -30 \leq mn \leq 35$$

If $$x<1$$ and $$3y=-3x+54$$, which of the following is true about $$y$$?

(A) $$\ \ y < -19$$
(B) $$\ \ y < 17$$
(C) $$\ \ y = 17$$
(D) $$\ \ y > 17$$
(E) $$\ \ y > 18$$

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