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: Understand the run rate definition. The run rate at the end of over k is given by:

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

From the table:

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

The additional runs scored in the (N − 1)-th and N-th overs are:

Runs in (N − 1) and N = 7.43N − 8(N − 2).

Simplify:

Runs in (N − 1) and N = 7.43N − 8N + 16 = −0.57N + 16.

Step 2: Verify conditions for N. Since the team did not score less than 6 runs or more than 15 runs in any over, the runs in (N − 1)-th and N-th overs must satisfy:

6 ≤ −0.57N + 16 ≤ 15.

Solve the inequalities:

1. −0.57N + 16 ≥ 6:
2. −0.57N + 16 ≤ 15:

Thus, N must be an integer between 7 and 13. Testing N = 13 satisfies all conditions.

Final Answer: 13.

Answer 2

Step 1: Understand the given conditions. The runs scored in any over are between 6 and 15. For a total of 22 runs in two overs, the possible pair of scores must add to 22.
Step 2: Identify the valid pair of scores. Possible pairs of scores satisfying x + y = 22 are: (7, 15),(8, 14),(9, 13),(10, 12),(11, 11).
Step 3: Match the pairs to the over numbers. Since the valid pairs of scores are within the given range of runs per over, 8 and 14 can be scored in overs 8 and 9.
Final Answer: 8 and 9.

Answer 3

Step 1: Analyze the run rates. The run rate decreases at N (from the table in Question 23).
This suggests that a relatively low number of runs was scored in over N − 1 or N.
Step 2: Identify the least runs scored. If N = 7 (from Question 23), the team must have scored the least number of runs in over 7, as the run rate drops at this point, indicating a minimum addition to the total.
Final Answer: 7.