Years ago I was teaching as an adjunct (not where I am currently teaching.) We were required to give a multiple choice final, supplied by the department. I liked the questions, but took the exam home to my husband and told him to look at a specific four of the fifty answer choices and come up with the answer, without looking at the questions. He was correct.
Regardless of the question, suppose the answers to a problem were
The answer probably involves a 2, which eliminates c) it probably is positive, which eliminates d) and is probably an integer, which eliminates a).
Multiple choice is often a bad idea, because students usually make more kinds of mistakes than can be listed as possible answers. Even if there are only four kinds of likely mistakes, the student can learn something from the answers given.
On the other hand, multiple choice questions are easier to grade, which is why they are given.