The three exams

The three exams

When the test results were published, one school saw that all of its 32 students passed at least one of the three exams each had taken.

Of the students who did not pass the exam 1, the number that passed the exam 2 was exactly half of those who passed the exam 3. The number of students who passed the exam 1 is the same as that of the students who only passed one of the other exams, and three more that passed exam 1 and at least one of the other exams.

How many students passed more than one exam?


11 students passed only test 1, 3 students passed only test 2 and 8 students passed only test 3. That means that 10 students passed more than one exam