Instructions: DO NOT USE CALCULATOR. Figures are not drawn to scale. If \(x > y > 1\), which of the following must be greater than x?
A. \(7y/5x\)
B. \(x/(2y-x)\)
C. \((x+y)/y\)
D. \(6x/(y+5x)\)
E. none of these
Explanation: (E) Test with \(x=10, y=2\) (\(10 > 2 > 1\)). (A) \(\frac{7y}{5x} = \frac{7 \cdot 2}{5 \cdot 10} = \frac{14}{50} < 10\). Not greater than x. (B) \(\frac{x}{2y-x} = \frac{10}{2 \cdot 2 - 10} = \frac{10}{-6}\) (Negative, so < 10). Not greater than x. (C) \(\frac{x+y}{y} = \frac{10+2}{2} = \frac{12}{2} = 6 < 10\). Not greater than x. (D) \(\frac{6x}{y+5x} = \frac{6 \cdot 10}{2+5 \cdot 10} = \frac{60}{52} < 10\). Not greater than x. Since none of the options must be greater than x, the answer is E.
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