The scientist hypothesized that the new drug (a) would (b) effectively treat the disease, (c) alleviating symptoms and (d) improving the patient's quality of life (e).
Correct: A
Since the verb used in the beginning of the sentence is "hypothesized," which is in past tense, and the question continues using the past tense and is about a hypothetical statement, the best answer would be "would effectively treat." Thus, (A) is correct.