Correct (on the typical assumptions we can only pick one answer, that the selection is uniformly random, etc.). The question is actually a fairly common paradox. The cause is the sort of self-referential nature of the question.
Typically for multiple-choice questions with four answers, at random there is a $25\%$ chance to get it right. But two answers have that choice.
So logically it would be $50\%$, but only one choice corresponds to that. So you're damned if you pick either one: if $50\%$ is correct, the odds are $25\%$ and if $25\%$ is correct the odds are $50\%$.
$60\%$ simply makes no sense, being not a multiple of $25\%$, and can be ruled out outright.
So as it is posed, there is no correct answer.