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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