National Institute of Management Lucknow (NIM-L) conducts its entrance test called National Admission Test (NAT) for admission to its flagship two-year MBA course. The QA section of NAT-2018 had 34 questions, all of which were multiple choice format questions. The following was the marking scheme for NAT-2018:
1. Each correct answer fetched 12 marks. There was negative marking for incorrect answers. For each incorrect answer, four marks were deducted from the score of a student.
2. Additionally, there was a progressive penalty for skipped questions, as specified in the table below:
For example, a student who skipped 6 questions lost 0 × 4 + 1 × (6 – 4) = 2 marks on account of these 6 skipped questions. Similarly, a student who skipped 18 questions lost 0 × 4 + 1 × 4 + 2 × 4 + 3 × 4 + 4 × 2 = 32 marks on account of these 18 skipped questions.
3. The exam is computerized and the questions are presented to students one at a time. Once a student sees the question, he/she has only two options before seeing the next question: either attempt the question or skip the question. After a student attempts/skips a question, the next question is presented and he/she is not able to revisit the questions that are already attempted/skipped.
4. All the questions that a student is unable to answer in the stipulated time of one hour are considered to be ‘skipped’ by the student. For example, if a student is able to answer only 30 questions in the section at the end of one hour, the remaining 4 questions in the section are considered to be skipped by the student.
5. Cumulative score of a student at the end of each question (considering the penalty on account of incorrect and skipped questions) is calculated. For example, if a student gets one answer correct, one answer incorrect and skips one question out of the first three, his/her cumulative score at the end of the 3rd question will be
12 – 4 – 0 = 8.
Similarly, the total score of a student at the end of the stipulated time is calculated after deducting the marks on account of penalty for the questions that were not visited by the student (and hence were considered to be skipped).
Q1)Which of the following cannot be a valid cumulative score that a student could have obtained at the end of 10 questions in that section?
Q2)Which of the following can be a valid score that a student could have obtained in the section if it is known that he/she attempted 28 questions in the section?
Q3)It is known that a student scored exactly 100 marks in the section.
What can be the maximum number of questions that the student could have attempted (either correctly or incorrectly) in the section? (Write 35 if it is not possible to score 100 marks in the section)
Q4)It is known that a student scored exactly 100 marks in the section.
What can be the minimum number of questions that a student could have attempted (either correctly or incorrectly) in the section? (Write 35 if it is not possible to score 100 marks in the section)