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(C) Let $x$ be the number of correct answers,$y$ be the number of wrong answers,and $z$ be the number of unattempted questions.Given that the total nu

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$6$

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(C) Let $x$ be the number of correct answers,$y$ be the number of wrong answers,and $z$ be the number of unattempted questions.Given that the total number of questions is $30$,we have $x + y + z = 30$.The total score is given by $4x + 0y + 1z = 60$,which simplifies to $4x + z = 60$.From the second equation,$z = 60 - 4x$.Since $z \ge 0$,we have $60 - 4x \ge 0$,which implies $x \le 15$.Also,since $x + y + z = 30$,we substitute $z = 60 - 4x$ to get $x + y + (60 - 4x) = 30$,which simplifies to $y = 3x - 30$.Since $y \ge 0$,we have $3x - 30 \ge 0$,which implies $x \ge 10$.Thus,$10 \le x \le 15$.The possible integer values for $x$ are $10, 11, 12, 13, 14, 15$.Counting these,there are $6$ possible values for $x$.

There are $30$ questions in a multiple-choice test. $A$ student gets $1$ mark for each unattempted question,$0$ mark for each wrong answer,and $4$ marks for each correct answer. If a student answered $x$ questions correctly and scored $60$,then the number of possible values of $x$ is:

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