Question

If group B contains 23 questions, then how many questions are there in Group C?

• A. 1
• B. 2
• C. 3
• D. Cannot be determined
• A. 11 or 12
• B. 12 or 13
• C. 13 or 14
• D. 14 or 15

Answer 1

The Correct Option is D

Given that group B contains 23 questions, the total number of questions is 100. Let the number of questions in group A be \(x\) and in group C be \(y\). We know: \[ x + 23 + y = 100 \quad \text{or} \quad x + y = 77 \] Also, the total marks from group A are at least 60% of the total marks. The total marks from each group are:
- Group A: \(x \times 1\)
- Group B: \(23 \times 2 = 46\)
- Group C: \(y \times 3\)
The total marks are \(x + 46 + 3y\), and this must be at least 60% of the total marks, i.e.: \[ x + 46 + 3y \geq 0.6 \times 100 = 60 \] This gives the equation: \[ x + 3y \geq 14 \] Since \(x + y = 77\), solving these two equations gives a range for \(y\), but the exact value cannot be determined. Therefore, the answer is (4) Cannot be determined. \[ \boxed{\text{Cannot be determined}} \]

Answer 2

We are given that group C contains 8 questions and that group B carries at least 20% of the total marks. The total number of marks is: \[ \text{Total marks} = 1 \times \text{questions in group A} + 2 \times 23 + 3 \times 8 \] Let the number of questions in group A be \(x\) and in group B be \(y\). We know: \[ x + y + 8 = 100 \quad \text{or} \quad x + y = 92 \] The total marks are: \[ \text{Total marks} = x + 46 + 24 \] Group B must contribute at least 20% of the total marks: \[ 2y \geq 0.2 \times (x + 70) \] Solving for \(y\) gives the possible values for the number of questions in group B as 12 or 13. \[ \boxed{12 \text{ or } 13} \]