siyer, thanks for pointing that out.
Here is the real OE (I have also replaced the incorrect explanation above):
Actual Answer : D
Explanation
There is a stark difference between the phrases 'a little' and 'the little,' as used in the context of this sentence.
Since the sentence talks of a specific nature of hope (that there was of revivingthe patient), the definite article 'the' must precede 'little hope.'
'A little hope' would be used in a more general sense, as for example, 'the advice of the doctor gave us a little hope.'
[Note : If you omit the 'a' in this sentence, it takes on a completely different meaning. 'Little hope,' without the 'a', implies 'almost negligible' hope, next to none. 'A little hope,' however, has a slightly more positive connotation.]
Knowing this, the first two options are ruled out.
Option C uses the unnecessary phrase 'that there was' while option e unnecessarily uses the passive voice, 'being revived'.
Be wary of the word 'being' in GMAT sentence, the evaluators seem to dislike it!
Hence (D) is the correct answer.