We can spot that Jack\textquotesingle s statement and Jimmy\textquotesingle s statement contradict each other, so one of them is telling the truth. Therefore, Sarah tells a lie. 
Jack, Sarah, and Jimmy participated in a Maths competition.  \textbf{Jack says: "I won the competition."}  \textbf{Sarah says: "I didn\textquotesingle t win the competition."}  \textbf{Jimmy says: "Jack didn\textquotesingle t win the competition."}  Only one of them told the truth. Who won the Maths competition? 
a) $$$$Jack 
b) Sarah 
c) Jimmy 