Given a student answers 50 percent of the questions on an exam correctly and 10 questions incorrectly, what was the total number of questions on the exam?
So we can first assume that the student answered all of the questions on this exam. If 50 percent of the questions were answered correctly, then this would mean that 50 percent of the questions were answered incorrectly. Because if the student answered all of the questions, whether they be correct or incorrect, answering all questions that would be 100 percent of the questions completed because 50 percent plus 50 percent would be 100 percent, the entire exam.
So we already use the fact that 50 percent of the questions on the exam were answered correctly. But we’re also told that 10 questions were answered incorrectly. So if 10 questions were answered incorrectly, that means 10 questions must represent 50 percent of this exam. So 50 percent is half of 100 percent. And if half of this exam was 10 questions and the other half, the other 50 percent that was answered correctly, would also have to be 10 questions.
Another way that we could think about this would be if 10 questions represented 50 percent of our exam, we would need to double that to get to 100 percent. So we’d have to multiply the 50 percent times two, which means we would have to multiply the 10 questions by two, therefore making the entire exam 20 questions long.
So whether we did 10 questions plus 10 questions equaling 20 questions for the entire exam or took 10 questions times two, there would be a total of 20 questions on the exam.