You're describing one small part of the family of damages (in the legal sense), and that isn't how common law works. To draw from the rich vocabulary of HN, think of the opportunity cost imposed by the time wasted on preparation and the test itself, that also has value beyond the entrance fee.
Putting that aside, you don't just sue for money, you can sue for different outcomes and injunctive relief. For example you could sue to have the results released as planned.
Under common law courts don't award speculative damages - i.e. opportunity cost. If you had concrete damages, like you bought a computer just to participate in this contest, you might theoretically have a claim for the cost of the computer... that's simply not realistically the case though.
Injunctive relief for not publishing known to be incorrect test rankings? Not likely.
A FOI request might get you access to the rankings if you really cared... I'm not quite sure what the contours of FIPPA (roughly equivalent to America's FOIA) is with regards to our universities but I believe it generally applies to them. At the same time it could easily fall within privacy limitations.
Putting that aside, you don't just sue for money, you can sue for different outcomes and injunctive relief. For example you could sue to have the results released as planned.