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Exam Ranking and Negative Marking Calculation

XAT 2015 · Quantitative Ability & Data Interpretation · Medium · Quantitative Ability

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In an examination, two types of questions are asked: one mark questions and two marks questions. For each wrong answer, of one mark question, the deduction is 1/41/4 of a mark and for each wrong answer, of two marks question, the deduction is 1/31/3 of a mark. Moreover, 1/21/2 of a mark is deducted for any unanswered question. The question paper has 10 one mark questions and 10 two marks questions. In the examination, students got all possible marks between 25 and 30 and every student had different marks. What would be the rank of a student, who scores a total of 27.5 marks?

  1. A.

    5

  2. B.

    6

  3. C.

    7

  4. D.

    8

  5. E.

    None of the above

Answer

A

Explanation

Maximum possible score = 10(1)+10(2)=3010(1) + 10(2) = 30. Deductions for various cases from 30:

  • Rank 1: All correct = 30
  • Rank 2: 1 wrong in 1-mark qn = 30−1.25=28.7530 - 1.25 = 28.75
  • Rank 3: 1 unattempted 1-mark qn = 30−1.5=28.530 - 1.5 = 28.5
  • Rank 4: 1 wrong in 2-mark qn = 30−2.33=27.6730 - 2.33 = 27.67
  • Rank 5: 2 wrong in 1-mark qn = 30−2(1.25)=27.530 - 2(1.25) = 27.5

Thus, a score of 27.5 corresponds to rank 5.

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