A is wrong.

B is wrong
C : correct

Rule : f you can replace the EXACTLY SAME verb/noun/.. then there is no need to repeat it.

B wrong
----------------
Actually B is equivalent to :

everybody works faster than I [works]. --> incorrect


You can avoid only those verbs which are exactly same.

e.g.

everybody works faster than John.

here it is fine to avoid the verb, because the complete sentence will be

everybody works faster than John [works].



everybody works faster than I .