Answer: The correct answer is more quickly: "Do lentils cook more quickly than pinto beans?".
Step-by-step explanation: In the sentence provided, there are two items that are being compared ("lentils" and "pinto beans"); therefore, a comparative form must be used. Comparative adjectives/adverbs are formed by adding the suffix "-er" at the end of the word or by including the word "more" before the adjective/adverb. In that way, "most quickest" and "most quickly" cannot fill in the blank because they represent superlative forms. Moreover, "more quicker" is an incorrect comparative form since "more" and "-er" cannot appear together. Therefore, the form that fills in the blank is "more quickly": the word "more" has been added before the adverb "quickly" in order to give place to the comparative form.