Understanding the Problem
We are given two inequalities involving variables $x$ and $y$ :
1. $x y<0$
2. $x-y>0$

And we have two quantities to compare:
- Quantity A: $|x|$
- Quantity B: $|y|$

We need to determine the relationship between Quantity A and Quantity B based on the given inequalities.

Analyzing the First Inequality: $x y<0$
The inequality $x y<0$ means that the product of $x$ and $y$ is negative. For the product of two numbers to be negative, one must be positive, and the other must be negative. So, this tells us that:
- Either $x>0$ and $y<0$, or
- $x<0$ and $y>0$.

In other words, $x$ and $y$ have opposite signs.

Analyzing the Second Inequality: $x-y>0$
The inequality $x-y>0$ can be rewritten as $x>y$. This means that $x$ is greater than $y$.


Combining Both Inequalities
Now, let's combine the information from both inequalities.
From $x y<0$, we have two cases:
Case 1: $x>0$ and $y<0$
Given that $x>y$, and since $y$ is negative, $x$ is greater than a negative number. This is always true if $x>0$, so this case holds.

In this case:
- $x>0$, so $|x|=x$.
- $y<0$, so $|y|=-y$.

From $x>y$, since $y$ is negative, $x>y$ doesn't directly tell us how $x$ compares to $-y$ (which is positive).

For example:
- Let $x=1, y=-2$. Then $x y=-2<0, x-y=3>0$.
- $|x|=1,|y|=2$. So $|x|<|y|$.
- Let $x=3, y=-1$. Then $x y=-3<0, x-y=4>0$.
$\circ|x|=3,|y|=1$. So $|x|>|y|$.
So, in this case, $|x|$ can be less than or greater than $|y|$.
Case 2: $x<0$ and $y>0$
Given that $x>y$, and $x$ is negative while $y$ is positive, this would mean a negative number is greater than a positive number, which is impossible (since any positive number is greater than any negative number).

For example:
- If $x=-1, y=2$, then $x>y$ implies $-1>2$, which is false.
- Similarly, any $x<0$ and $y>0$ will make $x>y$ false.

Therefore, Case 2 is impossible, and the only possible scenario is Case 1: $x>0$ and $y<0$.

Revisiting Case 1
From Case 1, we have $x>0, y<0$, and $x>y$.
We saw that $|x|=x$ and $|y|=-y$.
Now, $x>y$. Since $y$ is negative, $-y$ is positive, and $x$ is positive.
We can add $-y$ to both sides of $x>y$ :

$$
\(\begin{aligned}
& x+(-y)>y+(-y) \\
& x-y>0
\end{aligned}\)
$$


But this is just our original inequality, so it doesn't give us new information.
Alternatively, since $y$ is negative, $x>y$ is always true (any positive is greater than any negative), so this doesn't constrain the relationship between $x$ and $-y$.

From the examples earlier:
- $x=1, y=-2:|x|=1<|y|=2$.
- $x=3, y=-1:|x|=3>|y|=1$.

Thus, $|x|$ can be less than or greater than $|y|$, depending on the values.
Checking for Equality
Can $|x|=|y|$ ?
If $|x|=|y|$, then $x=-y$ (since $x>0, y<0$ ).
Then $x-y=x-(-x)=2 x>0$, which holds if $x>0$.
So, $|x|=|y|$ is possible (e.g., $x=1, y=-1$ : $x y=-1<0, x-y=2>0,|x|=|y|=1$ ).

Checking for Equality
Can $|x|=|y|$ ?
If $|x|=|y|$, then $x=-y$ (since $x>0, y<0$ ).
Then $x-y=x-(-x)=2 x>0$, which holds if $x>0$.
So, $|x|=|y|$ is possible (e.g., $x=1, y=-1$ : $x y=-1<0, x-y=2>0,|x|=|y|=1$ ).
Conclusion
From the possible cases:
- $|x|$ can be less than $|y|$.
- $|x|$ can be equal to $|y|$.
- $|x|$ can be greater than $|y|$.

Therefore, the relationship between Quantity A and Quantity B cannot be determined from the given information.

Final Answer
The relationship cannot be determined from the given information.