HELLO ....How many questions did the student answer in total?

Mark took a 50-question test in which he tested:
3 points are awarded for each correct answer,
0 points for each unanswered question
and subtract 1 point for each incorrect answer.
Mark got 117 points
he knows that the number of questions he didn't answer is less than the number of questions he answered incorrectly.
How many questions did the student answer in total?

1 Answer
May 30, 2018



Since 117/3 = 39, we know that at least 39 of the questions must have been answered correctly. Moreover, the number of questions answered correctly cannot be greater than 41 since otherwise the number of incorrect answers necessary to bring the score down to 117 would exceed the number of remaining questions (e.g. if 42 questions were correct, (42 x 3) - 117 = 9, which would require 51 questions).

Thus we have 3 possibilities for the number of correct answers:

39, 40, 41

Testing these out, we see that 39 correct would give 0 incorrect answers, 40 would give 3 incorrect answers and 41 would give 6 incorrect answers to bring the score back to 117. Since the number of incorrect answers is stated to be greater than the number of unanswered questions, the only possibility, however, is 41 correct answers, along with 6 incorrect answers and 3 unanswered questions:

41 x 3 = 123 (total score from correct answers)
123 - 6 = 117 (incorrect answers subtracted)
50 - (41 + 6) = 3 (unanswered questions)

Hence, the answer is 47 questions answered.