Q105
ArithmeticNumber System, LCM/HCF & Divisibility
In an examination, a student gets 4 marks for every correct answer, 1 for every unattempted question and 0 for every wrong answer. If there are 30 questions, which of the following total scores is not attainable by a student?
- a.113
- b.114
- c.115
- d.117
Answer: (C) 115
With $c$ correct, $u$ unattempted and the rest wrong ($c + u \le 30$), the score is $4c + u$. Scores of 113 ($c = 28$, $u = 1$), 114 ($c = 28$, $u = 2$) and 117 ($c = 29$, $u = 1$) are all possible. For 115 we would need $c = 28$ with $u = 3$ (31 questions) or $c = 29$ with $u = -1$, both impossible, so 115 cannot be scored. In fact, near the maximum of 120 the unattainable scores are 119, 118 and 115. Method for such questions: fix the number of correct answers at the highest value that does not overshoot, then see whether the remaining marks fit into the remaining questions.