Adverbs describe (or modify) verbs, adjectives and other adverbs, by telling us the manner, the way (how), the extent of a verb, adjective or another adverb.
For examples:
I ran fast. (fast - adverb, shows the manner of running, modifies 'ran' - verb)
She is a very good athlete. (very - adverb, modifies 'good - adjective)
I ran very quickly. (very - adverb, shows the extent, modifies 'quickly' - adverb)
The statement is thus, true.
Hence option A is correct and B is incorrect.