First find the number of students who went through breakups: 1/4 * 180 = <<1/4*180=45>>45 students
Then subtract that number from the total number: 180 students - 45 students = <<180-45=135>>135 students
Then divide that number by 3 to find the number of students who didn't show up to take the test: 135 students / 3 = <<135/3=45>>45 students
Then subtract the number of students who failed in each way from the total number to find the number who passed: 180 students - 45 students - 45 students - 20 students = <<180-45-45-20=70>>70 students
#### 70