I'm making a weighted test, i.e. a test with N yes/no questions where the score differs from question to question. For simplicity assume that the sum of all individual scores is 100 and assume the test is passed if the achieved score is 70 or more.
Now I like to make sure that all questions are relevant for passing/failing the test.
Simple example of good test:
Q1 gives 30 Q2 gives 30 Q3 gives 40
The test can be passed by the following correct answers: Q1+Q3, Q2+Q3 (and Q1+Q2+Q3) So all questions can be relevant for passing or failing.
Simple example of bad test:
Q1 gives 10 Q2 gives 45 Q3 gives 45
In this case it doesn't matter whether the answer to Q1 is right or wrong as it can't change the pass/fail result of the whole test.
So my question is:
In a N question test with a given list of scores per question how do I check that all questions can impact the pass/fail result of the whole test?
If I look at a specific answer with score S, I need to prove that some combination of right/wrong answers to the other questions can give a total score in the range [70-S:69]. But I'm not sure how to do that.