I have been advised to use Logistic Regression to solve the scenario described below. Can anyone confirm that Logistic Regression is the correct statistical methodology? Or provide suggestions for a better methodology?

Scenario

A test has 20 questions

Each test question is scored 1 to 10 (discrete)

Final Score is the sum of question scores (min: 20, max: 200)

Passing is a Final Score of 100+ (Failing is 99 or less)

I want to determine which of the 15 questions best predict an outcome of pass or fail

What I am NOT looking for

I don’t want a test that affirms that the whole is the sum of the parts. (Results show each question contributes 1/15th to the total score).

Examples of what I am looking for

Let’s say everyone (n=1000) who takes the test gets a 10 on question 1 and a 0 on question 2. Since everyone has the same score on questions 1 and 2, they are not very good predictors of outcome. Will Logistic Regression tell me which questions are POOR predictors of Pass/Fail? (Results say Q1 and Q2 are poor predictors).

Let’s say everyone who gets an 8 or more on Question #3 always passes the test. Will Logistic Regression tell me which predictors are BEST at predicting Pass/Fail? (Results show Q3 a very strong predictor).

Let’s say most people who gets an 8 or more on Question #4 pass. Will Logistic Regression quantify which predictors are BETTER than others? (Results show Q4 is a strong predictor, but Q3 is stronger).

Any input is much needed and greatly appreciated!

Thank you