Object a attracts object b with a gravitational force of 10 newton’s from a given distance. if the distance between the two objects is doubled, what is the new force of an attraction between them?

If the distance between two objects is doubled, then the gravitational forces between them become (1/2)² = 1/4 of the original gravitational forces.

If the magnitude of those forces was 10 Newtons before the move then they're 2.5 Newtons after it.

I changed the wording of the discussion to plural, because the wording in the question is misleading.  It shouldn't say "Object A attracts Object B" and then let it go at that.  Gravitational forces ALWAYS occur in equal pairs.  If Object B feels a pull of 10 Newtons toward Object A, then Object A feels a pull of 10 Newtons toward Object B.  

The masses don't even matter.  Gravity is always there equally in both directions.  Your weight on Earth is equal to the Earth's weight on you !

+15-35=-20

going in opposite directions