One of the greatest problems facing Engineering practitioners today,

Immediately you should recognize "apart from absorbing volumes of technical information and learning habits of scientific thought" is not part of the main core clause.

If you extract this out for a moment you will see the main clause is from the question is:

"One of the greatest problems facing Engineering practitioners today [...] empathetic to the needs of patients in the face of all the rigorous training".

In order to function as the main clause the above needs a verb that it is currently missing. Compare the end of each option, as this is the only part existing outside the above modifier we are temporarily ignoring and hence capable of affecting the main independent clause:

a) [...] is remaining
b) [...] is to remain
c) [...] which remain (can't act main clause verb since subordinated by which)
d) [...] and they remain (coordinating conjuntion "and" introduces new independent clause but does not provide the first independent clause with a verb it's currently missing)
e) [...] and besides remaining (no verb here to complete main clause, only present participle)

Option a) and b) are the only ones that could allow the main clause to be complete. Hence eliminate C,D,E.

Distinguish between a) and b) using //ism by now taking into account the part of the sentence we previously ignored. Hence a).

Hope this helps.