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

To find the value of \( N \), we have to solve the problem using the given conditions and information from the table.

The condition provided is:

• The expression for \( N \) is \(1 \leq N - 2 < N + 6 \leq 20\) and \( N \) is a positive integer.
• The table provides the run rate at specific overs \( N-2 \), \( N \), \( N+2 \), \( N+4 \), and \( N+6 \).
• The run rates given are: 
  - At \( N-2 \), the run rate is 8.00.
  - At \( N \), the run rate is 7.43.
  - At \( N+2 \), the run rate is 8.11.
  - At \( N+4 \), the run rate is 8.45.
  - At \( N+6 \), the run rate is 8.08.

Let's solve for \( N \):

1. Since \( 1 \leq N - 2 \), This implies \( 3 \leq N \).
2. Also, \( N + 6 \leq 20 \) which implies \( N \leq 14 \).

Therefore, \( N \) can take values between 3 and 14 inclusive.

Check the run rates condition:

1. The run rate at \( N-2 \) is slightly less than 8.00, but let's check a few values.
2. For meaningful differences in run rates and constant bounds of runs per over (6 to 15), computationally solving shows:

• Run Rate at N: Total runs scored in N overs = \( 7.43 \times N \)
• Run Rate at \( N-2 \): Total runs scored in \( N-2 \) overs = \( 8.00 \times (N-2) \)
• Run Rate at \( N+2 \): Total runs scored in \( N+2 \) overs = \( 8.11 \times (N+2) \)

Calculation:

To solve, assume certain values and verify. Checking pairwise differences from known over numbers, the arithmetic point comes valid for N = 7, fulfilling all constraints.

1. At \( N = 7 \): 
   - The condition holds 5.00 \( \leq \) \( N-2 = 5 \) (8.00 run rate)
   - The calculation matches exact settings with assumed run differences and rates aligning at known points.

Hence, the answer is the value of \( N \) is 7.

Answer 2

To determine the value of \(N\), consider the scenario provided in the question. We have a table showing the run rate of a cricket team at certain overs in a T20 match. The key condition given is:

• \(1 \leq N - 2 < N + 6 \leq 20\)
• Each over has a run count between 6 and 15 inclusive.

According to the table, the run rate at various overs is provided as follows:

Over Number	Run Rate
N-2	8.00
N	7.43
N+2	8.11
N+4	8.45
N+6	8.08

The condition \(1 \leq N - 2 < N + 6 \leq 20\) simplifies to:

• \(1 \leq N - 2\) and \(N + 6 \leq 20\)

This implies:

• \(3 \leq N\) (adding 2 to both sides of \(1 \leq N - 2\))
• \(N \leq 14\) (subtracting 6 from both sides of \(N + 6 \leq 20\))

Therefore, the possible values for \(N\) are from 3 to 14 inclusive.

Given the run rate at \(N\) is 7.43, we can calculate it using the formula for the average:

\[ \text{Run Rate} = \frac{\text{Total Runs}}{\text{Number of Overs}} \]

Let \(R_{n-2}, R_{n}, R_{n+2}, R_{n+4}, R_{n+6}\) represent the runs scored in overs \(N-2, N, N+2, N+4, N+6\) respectively. The total runs can be written as a system of equations based on the run rate values:

• \(R_{1} + R_{2} + \cdots + R_{N-2} = 8 \times (N-2)\)
• \((R_{1} + R_{2} + \cdots + R_{N-2} + R_{N-1} + R_{N})/(N) = 7.43\)
• \((R_{1} + R_{2} + \cdots + R_{N+2} + R_{N+3})/(N+4) = 8.45\)

Substitute and solve for possible \(N\). Checking each value from 7 to 14, we find:

• At \(N = 7\), calculations match the run rate. Therefore \(N = 7\).

Thus, the correct value of \(N\) is 7.

Answer 3

To solve this problem, we need to determine the correct pair of overs in which the team could have scored a total of 22 runs. We will use the provided data, specifically focusing on the calculation methods and understanding of the problem context.

Given data:

• Run rate at the end of \(N-2\)th over = 8.00
• Run rate at the end of \(N\)th over = 7.43
• Run rate at the end of \(N+2\)th over = 8.11
• Run rate at the end of \(N+4\)th over = 8.45
• Run rate at the end of \(N+6\)th over = 8.08

The problem provides the range of runs which can be scored in an over: 6 to 15. The total runs over two overs should be 22.

Let's examine the run rates and calculate possible runs:

1. For the pair (6 and 7): Examine the possible runs that could be scored: This pair does not provide valid solutions that sum up to 22 within the span limits.
2. For the pair (7 and 8): Similar to the above point, validating the run constraints, this does not sum up to 22.
3. For the pair (8 and 9): Once more, we check the limits and sum; they do not equal 22.
4. For the pair (9 and 10): We assess these overs with possible run combinations:
   • Possibility 1: 12 runs in the 9th over + 10 runs in the 10th over = 22 runs.
   • Possibility 2: 11 runs in the 9th over + 11 runs in the 10th over = 22 runs.
   • Possibility 3: 10 runs in the 9th over + 12 runs in the 10th over = 22 runs.
   Each possibility provides a sum of 22.
5. For the pair (10 and 11): Similarly, validating combinations for these overs, they don't add up to 22.

Through process of elimination and verification within the constraints, we establish that the correct answer is the pair of overs 9 and 10, which allows for a sum of 22 runs using the potential valid scores per over.

Therefore, the correct answer is: 9 and 10.

Answer 4

To solve this problem, we need to understand how the run rate changes across the overs mentioned in the table, and determine in which pairs of overs the team could have scored a total of 22 runs.

Step 1: Understand the Problem

Given the change in run rate across certain overs, the task is to identify during which over pairs a total of 22 runs were scored. The pair of overs given as options are: 6 and 7, 7 and 8, 8 and 9, 9 and 10, 10 and 11.

The constraints are that no over has less than 6 runs or more than 15 runs.

Step 2: Use the Given Data

From the table, we have certain information about run rates at different points. The run rate at the end of N+6 over is 8.08. Let us consider how this information helps us:

• If the run rate decreases, it means fewer runs were scored in that particular over relative to the average before it.
• Ensure the total number of runs scored in pairs of overs match 22, and abide by the constraints (6 ≤ runs ≤ 15).

Step 3: Try Different Over Pairs

Let's test the given over pairing options one by one:

• Option 6 and 7: If 6 runs in one over, maximum in the other is 15, and 6 + 15 = 21, which is less than 22.
• Option 7 and 8: Similarly, it cannot yield exactly 22 runs based on constraints.
• Option 8 and 9: Not feasible as 6 + 15 = 21, less than 22.
• Option 9 and 10: 7 and 15 add to 22, feasible under constraints (≤ 15).
• Option 10 and 11: Maximum score with minimal is less than 22, thus not possible.

Conclusion: Correct Option is 9 and 10

Therefore, after testing all the options, only "9 and 10" allows for an exact total of 22 runs.

Answer 5

To determine in which of the given overs the team must have scored the least number of runs, we need to analyze the run rate at different overs provided and apply logical reasoning.

The relevant data from the table is:

Over Number	Run Rate
N-2	8.00
N	7.43
N+2	8.11
N+4	8.45
N+6	8.08

1. At the end of over \(N-2\), the run rate was 8.00, which means the average runs per over was 8 across the overs from 1 to \(N-2\).
2. At the end of over \(N\), the run rate dropped to 7.43. This indicates that in the overs \(N-1\) and \(N\), the average runs per over dropped significantly.
3. The run rate at the end of over \(N+2\) increased to 8.11, suggesting an improvement in the scoring rate after over \(N\).
4. Given the constraints that the run rate cannot be less than 6 or more than 15 in any over, we evaluate the over where the least runs were definitely scored.
5. The drop in run rate from 8.00 at \(N-2\) to 7.43 at \(N\) is notable. This suggests that fewer runs were likely scored during these overs compared to the ones after \(N\), leading to a sharp decrease in the run rate.
6. Hence, among the provided options, over 7 could reasonably correspond to one of the spans where overs such as \(N-1\) and \(N\) occurred, which led to the least runs being scored to bring the average significantly down.

Therefore, the team must have scored the least number of runs in over 7.

Answer 6

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.