Carcass wrote:

The stem does not specify any number you could pick. As suc, pick a wise numebr to prove or disprove the quantities and see which answer is wrong or right.

\(\frac{1}{2}\) is just a wise number. This is the way to tackle a question like this as fast as possible.

hope is clear now

Regards

I thought it does restrict the numbers for x and y because (x-y) must equal 5 ( you therefore cannot pick 0.5 for both x and y because it would equal 0 if subtracted from one another)

The trick is to see that y can be negative (e.g. -4) while x positive (e.g. 1). This gives (x-y) = 5 and (x+y) = -3, multiplied gives -15 such that A would be smaller than B.

Now just picking two positive numbers to get (x-y) = 5 (e.g. x = 7 and y = 2) gives (x+y= = 9 and multiplied by 5 makes A larger than B.

Thus, answer D is correct

It's important to know that x²-y² can be rewritten to (x+y)(x-y).