For the DME arc rule, just remember the 1:60 rule (1 degree of arc at 60nm equals a ground distance of 1nm). The ratio is easy to scale down: 1 degree of arc at 30nm equals a ground distance of 1/2nm, 1 degree at 15nm equals a ground distance of 1/4nm, etc etc.
Eaxmple: Arc 70 degrees at 13DME
A 13nm arc is pretty close to 15. If I am arcing 70 degrees, just divide 70 by 4 (because at 15DME each degree is 1/4nm) and you get about 18 nm. No need to get fancy with calculators and what not. I had that exact question sprung on me at an interview. I think if I had asked for a pen and paper or a calculator I would have been laughed out of the room.