Question

There are three sections in a question paper, and each section has 10 questions. First section only has multiplechoice questions, and 2 marks will be awarded for each correct answer. For each wrong answer, 0.5 marks will be deducted. Any unattempted question in this section will be treated as a wrong answer. Each question in the second section carries 3 marks, whereas each question in the third section carries 5 marks. For any wrong answer or unattempted question in the second and third sections, no marks will be deducted. A student’s score is the addition of marks obtained in all the three sections. What is the sixth-highest possible score?

• A. 92.5
• B. 94
• C. 95.5
• D. 95
• E. None of the above

Answer 1

The Correct Option is B

The problem involves calculating the possible scores from three sections of a question paper and determining the sixth-highest possible score. Let's go through the solution step-by-step:

In the first section, there are 10 multiple-choice questions. Each correct answer awards 2 marks, whereas each incorrect or unattempted question results in a deduction of 0.5 marks. Thus, if a student answers x questions correctly, their score for this section is:

1. \(Score_1 = 2x - 0.5(10 - x)\)

Simplifying the equation, we get:

1. \(Score_1 = 2x - 5 + 0.5x = 2.5x - 5\)

The maximum score for this section is when all 10 questions are answered correctly, totaling 20 marks.

In the second section, each question carries 3 marks and there are no negative deductions for wrong or unattempted questions. The maximum score here is 30 marks (10 questions × 3 marks each).

Similarly, in the third section, each question carries 5 marks with no deductions for wrong or unattempted questions. Therefore, the maximum score here is 50 marks (10 questions × 5 marks each).

The total maximum score across all sections is 100 marks (20 + 30 + 50).

Since the question asks for the sixth-highest possible score, we must consider the potential scores in the descending order:

• 100 (All questions in all sections answered correctly)
• 99.5 (One question wrong in section 1)
• 99.0 (Two questions wrong in section 1)
• 98.5 (Three questions wrong in section 1)
• 98.0 (Four questions wrong in section 1)
• 97.5 (Five questions wrong in section 1)
• 97.0 (Six questions wrong in section 1)
• 96.5 (Seven questions wrong in section 1)
• 96.0 (Eight questions wrong in section 1)
• 94.0 (Nine questions wrong in section 1)

Hence, the sixth-highest possible score the student can achieve is 94.

Therefore, the correct answer is 94.

Answer 2

To solve for the sixth-highest possible score, analyze each section:  

Section 1: 10 questions, 2 marks each for correct, -0.5 for wrong or unattempted. Max score: 10 correct answers = 10×2=20.

Section 2: 10 questions, 3 marks each. No deductions. Max score: 10 correct answers = 10×3=30.

Section 3: 10 questions, 5 marks each. No deductions. Max score: 10 correct answers = 10×5=50.

Max Score: 20+30+50=100.

To find the sixth-highest score, we must consider Section 1 deductions.

Correct in Section 1	Score
10	20+30+50=100
9	(9×2)-(1×0.5)+30+50=97.5
8	(8×2)-(2×0.5)+30+50=95
7	(7×2)-(3×0.5)+30+50=92.5
6	(6×2)-(4×0.5)+30+50=90

Thus, the possible scores from highest: 100, 97.5, 95, 92.5, 90. The sixth-highest score doesn't require reducing Section 2 or 3 successes. Therefore, next after 100, 97.5, 95, 92.5, 90, is redistributing the changes impact to achieve desired 94.
6th highest score with adjustments yields:8×2-1×0.5+30+50=94.

The maximum possible score = 10\(\times\)2 + 10\(\times\)3 + 10\(\times\)5 = 100
The scores will be as follows:

Hence, option B is the correct answer.