A test consists of 120 questions. Each correct answer, each wrong answer and unanswered question in the test carry 1 Mark, 0.5 Mark and 0.25 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.
Please explain. Thank you
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nickey score 21 marks out of 30 for her mathematics test what fraction did she get correct
Let's break down the problem step-by-step:
1. Determine the scoring system:
- Correct answer: 1 mark
- Wrong answer: 0.5 mark
- Unanswered question: 0.25 mark
2. Calculate the total marks possible in the test:
- Each question carries 1 mark, and there are 120 questions, so the maximum possible marks are 120.
3. Given that the candidate scored 50 marks in the test, determine the number of correct answers:
- The candidate earned 1 mark for each correct answer.
- The total marks obtained is 50 marks.
- Therefore, the number of correct answers is 50.
4. Calculate the remaining marks after accounting for the correct answers:
- The candidate scored 1 mark for each correct answer, so the total marks obtained from the correct answers is 50 marks.
- Subtracting the total marks obtained from the possible maximum marks, we get the remaining marks: 120 - 50 = 70 marks.
5. Calculate the maximum number of questions that the candidate could have answered wrong:
- Each wrong answer leads to a deduction of 0.5 marks.
- To use up all the remaining 70 marks, we need to divide it by 0.5: 70 / 0.5 = 140.
- Therefore, the maximum number of questions that the candidate could have answered wrong is 140.
In conclusion, the candidate could have answered a maximum of 140 questions wrongly in the test if they scored 50 marks.
To find the maximum number of questions that the candidate could have answered wrongly, we need to consider the scoring system given: 1 mark for each correct answer, 0.5 marks for each wrong answer, and 0.25 marks for each unanswered question.
Let's assume the candidate answered a certain number of questions correctly, denoted by C. Then, the number of questions the candidate answered wrongly would be W, and the number of unanswered questions would be U.
We can use the given information about the scoring system to form an equation. Since the candidate scored 50 marks in total, we have:
Score = (1 * C) + (0.5 * W) + (0.25 * U)
Now we substitute the given values: Score = 50 and the total number of questions is 120.
50 = (1 * C) + (0.5 * W) + (0.25 * U)
To find the maximum number of questions the candidate could have answered wrongly, we need to minimize the number of unanswered questions since they carry fewer marks than wrong answers. Therefore, we will assume that the candidate answered all the unanswered questions correctly.
So, the equation becomes:
50 = (1 * C) + (0.5 * W) + (0.25 * 0)
Simplifying this equation, we get:
50 = C + 0.5W
Now, let's consider the total number of questions in the test. Since the candidate answered some questions correctly (C), answered some questions wrongly (W), and left some questions unanswered (U), the sum of these should be equal to the total number of questions, which is 120.
C + W + U = 120
Since we are looking for the maximum number of questions the candidate could have answered wrongly, we can assume the minimum number of correct answers (C) and unanswered questions (U).
Let's assume the candidate answered all questions correctly, i.e., C = 120 and U = 0. Substituting these values into the equation above, we get:
120 + W + 0 = 120
W = 0
This means that the candidate could have answered 0 questions wrongly in the test if he scored 50 marks.
Therefore, the maximum number of questions that the candidate could have answered wrongly is 0.