Question 8

Is $$[(x^{-1} - y^{-1} )/(x^{-2} -y^{-2}]>1$$?
I. x + y > 0
II. x and y are positive integers and each is greater than 2.

Solution

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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