Question

If $\frac{1}{x}$ is a positive fraction and $\frac{1}{y}$ is a negative fraction, then which of the following statements are true? (A) $\frac{1}{x} + \frac{1}{y}$ is positive (B) $\frac{1}{x} - \frac{1}{y}$ is positive (C) $\frac{x - y}{xy}$ is negative (D) $\frac{1}{xy}$ is positive (E) $\frac{1}{x^2} - \frac{1}{y^2}$ is positive

Choose the correct answer from the options given below:

Accepted Answer

B. Given $x > 0$ and $y < 0$. - (A) $\frac{1}{x} + \frac{1}{y}$: Sign depends on absolute values of $x$ and $y$. Not necessarily positive. - (B) $\frac{1}{x} - \frac{1}{y} = ext{pos} - ( ext{neg}) = ext{pos} + ext{pos} > 0$. Always true. - (C) $\frac{x - y}{xy}$: $x - y > 0$ (pos) and $xy < 0$ (neg), so $\frac{ ext{pos}}{ ext{neg}} < 0$. Always true. - (D) $\frac{1}{xy} < 0$. False. - (E) Sign depends on $|x|$ vs $|y|$. Not always true. Therefore, only (B) and (C) are true.

Positive and Negative Fractions Analysis

Explanation

Practise this under exam conditions