I'm not too sure of the exact regulations, but I think 20year olds had to register for the draft as well (I think those between 18 and 35 had to register, but it would be worthwhile to check the regulations).
The other son might already have served (do a search of the ancestry military records, not just in his home state as many ran away and enlisted elsewhere, and check different spelling of the surname as many mistakes were made by enlisting officials). In my research I have found in many cases the younger brother enlisted first, so he could have already joined up.
I'm sure that if there was a widowed mother with one able-bodied son left at home there was exemption from the draft.
I hope this helps, and good luck :)