Why is the radius of a positive ion always less than the radius of its neutral atom? (a) the nucleus pulls the remaining electrons in closer.
(b) the number of principal energy levels is always reduced. (c) the atomic orbitals contract all by themselves (d) electron speeds are reduced

Positive ions are positive because they have lost electrons.
(A)-This sounds accurate, but is actually not true. When an atom loses an electron and forms a positive ion, there will be less negative charge from the electrons to attract the positively charged nucleus. Losing electrons will actually decrease the attraction between the electrons and the nucleus.
(B)-This is true in some cases, but not all. If, for example, sodium were to lose an electron, it would drop down to having its largest orbital being in the second energy level, and would decrease in size. If magnesium were to lose an electron, it would still have one electron in the third energy level, so it wouldn't drop down an energy level.
(C) and (D)-Not sure where these answers even came from.

The actual reason behind the radius of a positive ion being smaller than the radius of its neutral atom is that the repulsive force between the electrons themselves is decreased, causing them to move closer together. 

Ibelieve y y even though i've only taken chemistry for one year

Hairy thick gross thing? idk