Everyone participating in the early sociological study committed a crucial methodological error by failing to fully consider alternative ways of classifying their data.

(A) by failing to fully consider alternative ways of classifying their
(B) by failing fully to consider alternative ways of classifying their
(C) they failed to consider alternative ways to classify their
(D) by not fully considering alternative ways to classify the
(E) by not considering fully alternative ways of classifying his or her
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The answer is E. The question tests for the correct form of the pronoun referring to the subject "everyone". The subject of the sentence is "everyone" and it is a singular indefinite pronoun. So it is the right antecedent for his or her in option E. All the other options have "their" as the pronoun referring to the singular subject "everyone".

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Everyone is singular. So pronoun should be singular. A, B, C are eliminated.

Between D and E, in E fully alternative ways doesn't make sense.