Hello Vjesus12.

Let's take a look at your question.

We need to find the value of |x-y|.

First Statement

1) x and y are integers

Here x and y can be any integer, so |x-y| will have different values. So, it is not sufficient.

Second Statement

2) xy=5

Here, x and y can be any real value whose product is 5, that is to say, we have the possible couples (1,5), (25, 1/5), (125, 1/25), . . . . and again, |x-y| will have different values. So, it is not sufficient.

First Statement + Second Statement

1) x and y are integers
2) xy=5

Now, we have that x and y are integers and their product is equal to 5.

Therefore, we get the cases : (1,5), (-1,-5), (5,1) and (-5,-1). For each couple of values, we will get $$\left|x-y\right|=\left|1-5\right|=\left|-4\right|=4.$$ $$\left|x-y\right|=\left|-1-\left(-5\right)\right|=\left|4\right|=4.$$ $$\left|x-y\right|=\left|5-1\right|=\left|4\right|=4.$$ $$\left|x-y\right|=\left|-5-\left(-1\right)\right|=\left|-4\right|=4.$$ So, we get only one value for |x-y|.

This implies that both statements together are sufficient.

Hence, the correct answer is the option C.

I hope it helps.