A wireless communication system and a terminal providing a wireless communication service and to a method by which a base station and a terminal transmit and receive data in an evolved universal mobile telecommunications system (E-UMTS) evolved from universal mobile telecommunications system (UMTS) or a long term evolution (LTE) system, are disclosed. In transmitting RACH MSG 3 by a terminal to a base station, the terminal transmits the RACH MSG 3 by applying different cyclic redundancy checks (CRCs) according to types of data included in the RACH MSG 3, to thereby reduce overhead of a medium access control protocol data unit (MAC PDU) included in the RACH MSG 3.