CAT Quant Practice Problems

Question: Is \(\left[ {\frac{{\left( {{x^{ - 1}} - {y^{ - 1}}} \right)}}{{\left( {{x^{ - 2}} - {y^{ - 2}}} \right)}}} \right] > 1?\)

I. x + y > 0.

II. x and y are positive integers and each is greater than 2.


  1. If the question can be answered with the help of statement I alone,
  2. If the question can be answered with the help of statement II alone,
  3. If both, statement I and statement II are needed to answer the question, and
  4. If the statement cannot be answered even with the help of both the statements.

Correct Option:2

Given equation can be resolved to $\frac{1}{\frac{1}{x} + \frac{1}{y}}$ ($xy \neq 0$ and $x \neq y$ )
Now for $\frac{1}{\frac{1}{x} + \frac{1}{y}}$ to be greater than 1,
1/x + 1/y has to be less than 1.
For this to be true both x and y should be greater than 2.
Statement I doesn’t give any information about this,
but statement II clearly specifies this. Hence, only
statement II is required to answer the given question.
So it can be answered using statement 2 alone.


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