Question

In the given question, there are two statements marked I and II. Decide which of the statements are sufficient to answer the question. Choose your answer from the given alternative.

Is $x<y$ ?
(I) $\frac{1}{x}<\frac{1}{y}$
(II) $\frac{x}{y}<0$

• A. Statement I alone is sufficient to answer the problem.
• B. Statement II alone is sufficient to answer the problem.
• C. Statement I and II both are needed.
• D. Statement I and II both are not sufficient.

Answer 1

The correct option is C Statement I and II both are needed.

(1) INSUFFICIENT: The meaning of statement (1) depends on the signs of $x$ and $y$. If $x$ and $y$ are either both positive or both negative, then you can take reciprocals of both sides, yielding $x>y$.

However, this statement could also be true if $x$ is negative and $y$ is positive in that case $x<y$

(2) INSUFFICIENT: Statement (2) tells you that the quotient of $x$ and $y$ is negative. In that case, $x$ and $y$ have different signs: one is positive and the other negative. However this does not tell you which one is positive and which one is negative.

(1) and (2) SUFFICIENT: Combining the two statements, if you know that the reciprocal of $x$is less than that of $y$ and that of $y$ and that $x$ and $y$ have opposite signs, then $x$ must be negative and $y$ must be positive, so $x<y$