In spite of Tom wanting to study, his sister made him wash the dishes.

(A) In spite of Tom wanting to study, his sister made him wash the dishes.
(B) In spite of the fact that Tom wanted to study, his sister made him wash the dishes.
(C) In spite of Tom's need to study, his sister made him wash the dishes.
(D) In spite of Tom's wanting to study, his sister made him wash the dishes.
(E) In spite of Tom studying, his sister made him wash the dishes.

(A) This is not correct. Choice A is incorrect because the possessive form of the noun ("Tom's") must be used to modify the gerund ("wanting").

(B) This is not correct. Choice B is too wordy.

(C) This is not correct. Choice C changes the meaning of the original sentence.

(D) You are right. Choice D is correct.

(E) This is not correct. Choice E is incorrect for the same reason that Choice A is incorrect. Also, Choice E changes the meaning of the original sentence.