susheelh wrote:
Given that \(ab< 0\) and \(a > b\), which of the following must be true?
I. \(a>0\)
II. \(b>0\)
III. \(\frac{1}{a} > \frac{1}{b}\)
A. I only
B. II Only
C. I and III Only
D. II and III Only
E. I, II and III
\(ab< 0\) means that a and b have different signs. Since also given that a > b, then a > 0 > b (a and b have different signs).
So, I is true and II is not.
Next, 1/a = 1/(positive) = (positive) and 1/b = 1/(negative) = (negative), thus 1/a > 1/b. III is true too.
Answer: C.
Hope it's clear.
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