Question

What is the value of N?

• A. 7
• B. 13
• C. 14
• D. 9
• E. 12
• A. 6 and 7
• B. 7 and 8
• C. 8 and 9
• D. 9 and 10
• J. 10 and 11
• A. 7
• B. 8
• C. 9
• D. 10
• O. 11

Answer 1

The Correct Option is A

Step 1: Define and calculate run rate. The run rate after k overs is computed as:

Run Rate at k = $\frac{\text{Total runs scored in overs 1 to } k}{k}$

Based on the provided data:

• At over N − 2, the run rate is 8.00.
• At over N, the run rate is 7.43.

The total runs scored in overs (<i>N</i> − 1) and N can be determined by the change in total runs:

Total runs in overs (<i>N</i> − 1) and N = (Run Rate at N × N) − (Run Rate at N − 2 × (<i>N</i> − 2)).

Substituting the given values:

Runs in (<i>N</i> − 1) and N = 7.43N − 8(<i>N</i> − 2).

Simplify the expression:

Runs in (<i>N</i> − 1) and N = 7.43N − 8N + 16 = −0.57N + 16.

Step 2: Determine valid range for N. Given that the team scored between 6 and 15 runs per over, the runs in overs (<i>N</i> − 1) and N must fall within this range:

6 ≤ −0.57N + 16 ≤ 15.

Solve the inequalities independently:

1. For the lower bound: −0.57N + 16 ≥ 6
2. For the upper bound: −0.57N + 16 ≤ 15

The solution to these inequalities indicates that N must be an integer between 7 and 13, inclusive. The value N = 13 satisfies all the given conditions.

Final Answer: 13.

Answer 2

Step 1: Analyze Constraints. Runs per over range from 6 to 15. The sum of runs over two overs must equal 22.

Step 2: Determine Valid Score Combinations. Pairs of scores that sum to 22 and fall within the allowed range per over are: (7, 15), (8, 14), (9, 13), (10, 12), (11, 11).

Step 3: Assign Scores to Overs. Given the valid score pairs are within the specified per-over run range, scores of 8 and 14 can occur in overs 8 and 9 respectively.

Final Answer: Overs 8 and 9.

Answer 3

Step 1: Analyze run rates. The run rate declines at over N (refer to the table in Question 23). This implies that a minimal quantity of runs was accumulated in over N − 1 or N. Step 2: Determine the lowest run accumulation. Given N = 7 (as per Question 23), the team must have scored the fewest runs in over 7, since the run rate decreases at this interval, signifying a minimum increase to the cumulative score. Final Answer: 7.