In a test, (+4) marks are given for every correct answer and (−2) marks are given for every incorrect answer. (a) Anita answered all the questions in the test. She scored 40 marks even though 15 of her answers were correct. How many of her answers were incorrect? How many questions are in the test? (b) Anil scored (−10) marks even though he had 5 correct answers. How many of his answers were incorrect? Did he leave any questions unanswered?
Anita had 10 incorrect answers. The test has 25 questions.
Anil had 15 incorrect answers. We cannot determine if he left questions unanswered without knowing the total number of questions.
Explanation
(a) Marks from correct answers = = 60. Total marks = 40. So marks lost = 60 − 40 = 20. Number of incorrect answers = 20 ÷ 2 = 10. Total questions = 15 + 10 = 25. (b) Marks from correct answers = = 20. Total marks = −10. So marks lost = 20 − (−10) = 30. Number of incorrect answers = 30 ÷ 2 = 15.