What is the equivalent of "make sense" in Chinese?
The most appropriate translation to make sense would probably be 有道理, which literally means has sense or reason.  For example:
你说的有道理
What you said is reasonable / What you said makes sense.

The phrase 说不通 would probably work, but it is not used frequently in Mainland China Mandarin (普通话) as 有道理 for the same context, if at all.
As for 符合逻辑, the phrase means the same thing as 有道理, but it is more verbose and academic.  It is like saying:
That is well reasoned. 
---as opposed to---
That makes sense.

As you can see the latter is what people use in daily conversations, while the former make you sound like some College Professor. ;-)
[It doesn't make any sense] would translate to 这没有道理。  Though in the context of your example, I think it sounds more natural in the Chinese context to say It is ridiculous (这太荒唐了） in response to the situation. Cultural differences in the way we think I suppose.