is there any shortcut other than working out for the 3 choices ?
It´s not necessary to work out all the choices, you just have to check the answer choices. In general, you start with the choice that repeats itself in most of the answer choices (so if it doesn´t hold, you can discard right away the largest # of answer choices). In this case, it´s III. If you solve for III first, and it holds, you can discard answer choice A and B right away. Then you are left with D and E. If you solve for II, and it holds, E is the answer, but if it doesn´t hold (this particular case), then the answer is D.