Shakespeare’s Hamlet was based on a style of morality plays, wherein personifications of vice and virtue fight over a man’s soul; Shakespeare’s originality
lay in the fact that he integrated these personifications into the internal psyche of the protagonist.
(A) lay in the fact that he integrated these
(B) lay in the fact of his integrating these
(C) laid in the fact of his integrating these
(D) lay in his integration of these
(E) laid in his integration of these
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Meaning is crucial to solve the question. Answer choices can be easily split between ''lay'' and ''laid''. All the choices have ''these'', so there is no point of worrying about pronoun ambiguity (at least with ''these''). First sentence ends with semicolon, so, there should be an independent clause after semicolon. So, lets take a look at answer choices.
A - ''He'' cant refer to ''Shakespear's hamlet or Shakespear's originality''. Besides , '' in the fact that'' looks redundant - lets keep it untill we find a better option.
B - '' in the fact of his integrating''. Between ''his integrating'' and ''his integration'', the latter is better. In this context, use of '' his integrating'' is not logical. B is out.
C - use of past simple, it means that originaliy laid in the past and it is not valid anymore. Intended meaning is distorted. C is out.
D - the answer choice does not distort the intended meaning and it is to the point. Lets keep it.
E - The same use of ''past simple'' as in C. E is out.
Between A and D , D gives more concise meaning. So, D is our winner.
Hope it helps.