The problems are simply too darn easy for people with lots of background knowledge. Eliminating obviously wrong answers usually got me the right answer even if I didn't know the material.
So, multiple choice questions are easier to hack than other kinds of questions, but if you "guess" the right answer 80% of the time, that's not really guessing. I think you underestimate the degree to which lots of background knowledge implies lots of subject knowledge / how much autodidactic knowledge clever people pick up just by paying attention and being curious.
(My school didn't offer Econ classes, but I took both AP Econ tests with about a day's worth of prep with an exam book, and believe I got 5 on both of them. Not surprising for someone who read econ books for fun and argued about economics on the internet in his spare time!)
So, multiple choice questions are easier to hack than other kinds of questions, but if you "guess" the right answer 80% of the time, that's not really guessing.
It depends how obvious it is that some of the answers are wrong.
When I was in high school, I noticed is that it was possible to score the top mark on an Advanced Placement (AP) Exam by answering a relatively small portion of the questions correctly.
During my junior year, I self-studied calculus, and took the AP Calculus AB exam. I was very surprised that I scored a 5 (the top mark), because at the time when I took the exam, I didn't know some very basic things that were on the syllabus.
The College Board gives the raw score to AP score conversions for the exams that have been most recently released. The percentages needed to get a 5 are as follows: