an exam has 120 questions.each correct question carries 1 mark.each wrong answer is penalized by 1/3rd of a mark and each unanswered question is penalized by 1/6th of a mark.a student who attempted the exam scored 60 marks.the minimum number of answers that the student could have gone wrong is??
Answers
minimum number of answers that the student could have gone wrong = 3
Step-by-step explanation:
Exam Has 120 Question
Correct Answers = X
Wrong Answers =Y
Unanswered Questions = 120 - X - Y
Marks for correct Answers = X
Marks Deducted for wrong Answers = Y/3
Marks Deducted for unanswered Questions = (120 - X - Y)/6
X - Y/3 - (120 - X - Y)/6 = 60
=> 6X - 2Y - (120 - X - Y) = 360
=> 6X - 2Y - 120 + X + Y = 360
=> 7X - Y = 480
=> 7X = 480 + Y
480/7 ≈ 68.6
Y is minimum so next number Divisible by 7 after 480 should be 7X
69 * 7 = 483
483 = 480 + Y
Y = 3
Correct Answer = 69 Marks = 69
Wrong answers = 3 Marks Deducted = 1
Unanswered = 48 Marks Deducted = 8
minimum number of answers that the student could have gone wrong = 3
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