They don't have any girlfriends at all.

Good thinking
The correct solution is usually the simplest one.

No, that doesn't work. There is a much more straightfotward solution! It dorsn't have to be girl friends. Look, it could just as well be the following: Bob claims to have twice as much money as Bill, and Bill says that they both have the same amount of money, yet both of them are right. How can that be?

Raymond

*wiping drool off chin* My brain hurts.

Bob has Euros and Bill has dollars ?

I'll give you a hint: From the information given about the girl friends, one can deducr exactly how many girl frieds each one has, and in the variant I gave involving money instead of girl friends, one can deduce exactly how much money each one has!
Raymond

Each have four girlfriends, but one folds his girlfriends in half, thus doubling the amount

Ah cute. Bob has two (twice as many as Bill which counts for one here). Bill has none, and together they have two. That is sneaky indeed, the keyword we tend to overlook is "they".

I liked Adam's answer better as that is mathematic and does not depend on word semantics. And mine, because it is kinda funny (at least I thought that when posting )

Joufa, there is no reason why in your solution, the number 4 should work better than any other number-- it could just as well be that each brother has ten, and one of the brothers folds five of them in half! I told you that from the information I gave, it is deducible exactly haw many each has, and there is only ONE possible solution!
Raymond

Hmmm...this is a good question. Then, with my last gasp, I would like to ask: do imaginary girlfriends count?

Juufa, No; imaginary girl friends do NOT count!Now really; can't you think of a number such that twice the number is the same as the number itself?
Raymond

1? 1 x 1 = 1...

That seems to work...

Juufa, No, the number 1 doesn't work. Twice 1 is not the sam as 1X1. Twice 1 is i+i, which is 2. In general, for any number n, twice n is not nXn , but n+n. For example, twice 5 is certainly not 5X5 (which is 25), but 5+5, which is 10.
Raymond

whoops... read the question wrong...