A test has 50 questions. A student scores 1 mark for a correct answer, -1/3 for a wrong answer, and –1/6 for not attempting a question. If the net score of a student is 32, the number of questions answered wrongly by that student cannot be less than? radio_button_unchecked 6 radio_button_unchecked 12 radio_button_unchecked 3 radio_button_unchecked 4
Question
A test has 50 questions. A student scores 1 mark for a correct answer, -1/3 for a wrong answer, and –1/6 for not attempting a question. If the net score of a student is 32, the number of questions answered wrongly by that student cannot be less than?
radio_button_unchecked 6
radio_button_unchecked 12
radio_button_unchecked 3
radio_button_unchecked 4
Solution
Let's denote the number of correct answers as C, the number of wrong answers as W, and the number of unattempted questions as U.
We know that:
C + W + U = 50 (since there are 50 questions in total)
We also know that the net score is 32, and the score is calculated as follows:
1C - 1/3W - 1/6*U = 32
We can substitute the first equation into the second to get:
1C - 1/3W - 1/6*(50 - C - W) = 32
Solving this equation for W (the number of wrong answers), we get:
W = 3*(50 - 2C - 332)
The minimum value of W (the number of wrong answers) occurs when C (the number of correct answers) is maximized. The maximum value of C is 50 (if all questions are answered correctly), so:
W_min = 3*(50 - 250 - 332) = -114
However, the number of wrong answers cannot be negative, so the minimum number of wrong answers is 0.
Therefore, the number of questions answered wrongly by the student cannot be less than 0.
However, this is not an option in the multiple choice answers provided. This suggests that there may be a mistake in the question or the answer choices.
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