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.
