Explanation:Concepts Tested: Verb tense, Modifier, Grammatical construction
A) Correct.
B) "Which" is illogically modifying "United States". The sentence became fragment by introducing "which" -- there is no main verb in the sentence.
C) Incorrect use of past perfect tense. There were two events in the past -- earlier event happened in 1870s and that event is associated with "had". So the later event, happened in 1920s, need to use simple past tense "were".
D) Placement of "throughout the United States" incorrectly suggests that women had voted as early as the 1870s throughout the United States. Original meaning of the sentence is that "voting rights for women throughout United States were not established until 1920". Incorrect use of "being".
E) Placement of "for women" is incorrect. Instead of saying "voting rights for women", the sentence is saying "United States for women". Also, the sentence has incorrect use of past perfect tense as stated in option C.
Correct answer is A.