Problem 117

1. First, let's translate the given solution from Chinese to English.

"$x > y > 0$" implies "$\frac{x}{y} > 1$", but the converse is not true. For example, if we take $x = -2$ and $y = -1$, then "$\frac{x}{y} > 1$" holds, but "$x > y > 0$" does not.

Thus, "$x > y > 0$" is a sufficient but not necessary condition for "$\frac{x}{y} > 1$".

Therefore, the answer is (C): Sufficient but not necessary condition.

2. Now, let's format the translated solution using Markdown and LaTeX.

"$x > y > 0$" implies "$\frac{x}{y} > 1$", but the converse is not true. For example, if we take $x = -2$ and $y = -1$, then "$\frac{x}{y} > 1$" holds, but "$x > y > 0$" does not.

Thus, "$x > y > 0$" is a sufficient but not necessary condition for "$\frac{x}{y} > 1$".

Therefore, the answer is (C): Sufficient but not necessary condition.

3. Next, let's enhance the solution by breaking it down into steps and providing additional explanations.

Step 1: Consider the given statement "$x > y > 0$". This implies that both $x$ and $y$ are positive, and $x$ is greater than $y$.

Step 2: Dividing both sides of the inequality by $y$ (which is positive), we get $\frac{x}{y} > 1$.

Step 3: Now, let's consider the converse, "$\frac{x}{y} > 1$". If we take $x = -2$ and $y = -1$, then $\frac{-2}{-1} = 2 > 1$, but $-2 > -1 > 0$ is not true.

Step 4: Therefore, "$x > y > 0$" is a sufficient but not necessary condition for "$\frac{x}{y} > 1$".

Step 5: The answer is (C): Sufficient but not necessary condition.

4. Finally, let's highlight the final answer using \boxed.

Therefore, the answer is \boxed{(C): Sufficient but not necessary condition}.