Question: Is average of the largest and the smallest of 4 given numbers greater than the average of the 4 numbers?

Statement-I: The difference between the largest and the second largest numbers is less than the difference between the second smallest and the smallest of the numbers.

Statement-II: The difference between the largest and the smallest numbers is greater than the difference between the second largest and the second smallest of the numbers.

Given:

Statement 1: The difference between the largest and the second largest numbers is less than the difference between the second smallest and the smallest of the numbers.

Statement 2: The difference between the largest and the smallest numbers is greater than the difference between the second largest and the second smallest of the numbers.

Let's analyze each statement:

Statement-I: The difference between the largest and the second largest numbers is less than the difference between the second smallest and the smallest of the numbers.

This statement doesn't provide direct information about whether the average of the largest and smallest numbers is greater than the average of all four numbers.

Statement-II: The difference between the largest and the smallest numbers is greater than the difference between the second largest and the second smallest of the numbers.

Similarly, this statement also doesn't directly give us the comparison of the averages.

Now, let's combine the statements:

By combining both statements, we understand that the differences between the largest and smallest numbers and between the second largest and second smallest numbers are related. However, this information alone doesn't allow us to determine whether the average of the largest and smallest numbers is greater than the average of all four numbers.

Therefore, the correct answer is option 4) if the question cannot be answered even by using both the statements together.