Bunuel
If \(x > y\) and \(\frac{1}{x} < \frac{1}{y}\), which of the following could be true:
I. \(0 < x < 1\) and \(0 < y < 1\)
II. \(xy < 0\)
III. \(-1 < x < 0\) and \(-1 < y < 0\)
A. I only
B. I only II only
C. II only III only
D. I only III only
E. I, II, and III
Are You Up For the Challenge: 700 Level QuestionsA very straight forward answer will be
\(x > y\) and \(\frac{1}{x} < \frac{1}{y}\),
that is cross-multiplication is NOT changing the sign. MEANS
both x and y have SAME sign or xy>0.I. \(0 < x < 1\) and \(0 < y < 1\)...xy>0..YES
II. \(xy < 0\)...NO
III. \(-1 < x < 0\) and \(-1 < y < 0\)...xy>0..YES
I and III
D
OR
Choose values...I. \(0 < x < 1\) and \(0 < y < 1\)..........x=0.9 and y=0.3...0.9>0.3 and \(\frac{1}{0.3}>\frac{1}{0.9}\)..\(\frac{10}{3}>\frac{10}{9}\)...YES
II. \(xy < 0\)....x=2 and y=-1...2>-1 but 1/2>1/-1...Eliminate
III. \(-1 < x < 0\) and \(-1 < y < 0\)....x=-0.3 and y=-0.9...-0.3>-0.9 and \(-\frac{1}{0.3}>-\frac{1}{0.9}\)..\(\frac{10}{3}>\frac{10}{9}\)...YES