Nuțu-Gajić represented Romania in seven Chess Olympiads from 1978 to 1994 and won five medals in total. She scored 7.5/10 in the 24th Chess Olympiad in Valletta 1980, and won the gold medal on board 3. She then improved on this by scoring 11/12 in the 25th Chess Olympiad in Lucerne 1982, to win the individual gold medal on board 3, and the team silver medal. She also helped Romania win two team bronze medals in Thessaloniki 1984 and Dubai 1986. She also won against former Women's World Chess Champion Nona Gaprindashvili at the 1992 Olympiad in Manila.