A test consists of 120 questions. Each correct
answer, each wrong answer and each unanswered
question in the test carry 1 mark, – 1/2 mark and
1/4 mark respectively. Find the maximum number
of questions that the candidate could have answered
wrongly in the test, if he scores 50 marks in it.
(1) 40
(2) 42
(3) 45
(4) 46
(5) 48
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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