Inequalities $A<B<C$, is combining the solutions of any 2 of the individual inequality $A<B$, $B<C$ or $A<C$ sufficient

Question

In the inequalities $A<B<C$, is combining the solutions of any 2 of the individual inequality $A<B$, $B<C$ or $A<C$ sufficient to solve the question. Or do I need to solve all 3 inequalities and then combining them together to get the answer?

Answer 1

The inequalities $A<B$ and $B<c$ are sufficient. It automatically follows that $A<C$ by the transitivity of the ordering. Solving only $B<C$ and $A<C$ is not enough, because we then do not know anything about how $A$ and $B$ are related. Similarly, $A<B$ and $A<C$ are not sufficient.