Determine Sufficiency of Expressions with Two Numbers

Medium Data Sufficiency Determining Sufficiency

Two numbers, $x$ and $y$, are such that $x > y > 0$. We want to determine if the value of the expression $E =\frac{x}{y} +\frac{y}{x}$ is greater than 2.

Statement (1): The product of $x$ and $y$ is $xy = 1$.

Statement (2): The difference between $x$ and $y$ is given by $x - y = 2$.

Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

Both statements together are sufficient, but each statement alone is not sufficient.

Each statement alone is sufficient.

Hint

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