If $\lceil\frac{x}{3}\rceil < \lceil\frac{y}{3}\rceil$ what can you conclude about $x$ and $y$? Certainly if there were no ceiling functions around I would know what that inequality implies. I'm just not sure what else I have to be worried about.
My intuition tells me that I should just be able to conclude that $x<y$, however I'm concerned there's more to the ceiling function than meets the eye. I know that if the input is an integer the function will return itself, if it's not an integer it will round up to the nearest integer.
Edit: Certainly if $x<y$ then it's not necessarily true that $\lceil\frac{x}{3}\rceil < \lceil\frac{y}{3}\rceil$. For example take $x=2$ and $y=3$, obviously $x<y$ but $\lceil\frac{x}{3}\rceil = \lceil\frac{y}{3}\rceil$.

The most general conclusion you can draw is that there exists an integer $n$ such that $x\le 3n< y$.
