To solve this question, the user needs to know the rules of adverb comparison.

In this sentence, we need to use an adverb to describe how we ran. The base form of the adverb "quickly" is used to compare two or more things.

Now, let's go through each option and explain why it is right or wrong:

A. quickly: This option is correct. "Quickly" is the correct form of the adverb in this sentence.

B. most quickly: This option is incorrect. We use "most + adjective" to form the superlative degree, but "quickly" is an adverb, not an adjective.

C. more quickly: This option is incorrect. We use "more + adjective" to form the comparative degree, but "quickly" is an adverb, not an adjective.

D. much quickly: This option is incorrect. We use "much + adjective" to intensify the meaning of an adjective, but "quickly" is an adverb, not an adjective.

The Answer is: A