【正确答案】 C

【答案解析】此题属于语义搭配题。此处需与句中宾语each other 搭配的短语，选项[C] compete against sb (与某人竞争)，符合题意。其他选项[A]compete for sth．[B] compete in a race 和[D] compete over sth．均属搭配不当。