The correct answer is (E).
There are two clauses in this sentence: the dependent beginning with the word "unlike" and the independent, which begins after the comma. The word "unlike" gives us the clue that the two sisters are very different in nature: one rarely speaks, while Amy talks a lot. The first blank will need a word that means "quiet," and the second needs a word that means "talkative."
Choice (E) is the correct answer because the first word describes Amy's quiet sister ("laconic") and the other describes chatty Amy ("loquacious"). Choice (A) cannot work because it contains two words that both describe Amy, since "effusive" is a synonym for "talkative." While "taciturn" ("quiet") in choice (B) fits, "banal" or "dull" does not. "Intransigent" from choice (C) does not work in our sentence, and while Amy may be "fascinating," that does not match the definition needed. Choice (D) is not the answer because while "garrulous" does describe someone who tends to talk a lot, "innocuous" means "harmless."