Accurately measuring the performance of someone who is not interested in demonstrating their performance seems like an impossible task for anyone but GLaDOS from the Portal series. ;)
More seriously, random pattern matching questions are the best you can do to control for the not-caring factor, because they eliminate the advantage of test prep. The SAT has a significant test prep factor, which I agree is highly confounded by "culture" (a byword for how much your parents make you study) and the circumstances and opportunities related to test prep, including the motivation of the student, and the availability of a place to study and study materials. IQ tests are significantly more meritocratic than algorithms interviews or the SAT.