That doesn't necessarily work because wrong answers can have natural correlations. Let's say you have two questions about finding a slope on an exam. Anyone who

That doesn't necessarily work because wrong answers can have natural correlations. Let's say you have two questions about finding a slope on an exam. Anyone who thinks that slope is change in x over change in y is going to get both of those questions wrong in the same way, even if those wrong answers are both individually rare. It would be really hard to distinguish between when these correlations are expected and when they're unexpected.