Directions (1-4): A number arrangement machine when given an input line of words and numbers rearranges them following a particular rule in each step. The following is an illustration of input and rearrangement.

Input: 28465    79784    63452    34867    93275

Step I: 52684    84797    24536    67843    57239

Step II: 24536    57239    52684    67843    84797

Step III: 4    25    36    49    64

Step IV: 20    115    250    385    540

Step V: 460    2645    5750    8855    12420

And Step V is the last step of the arrangement. As per the rule followed in the above steps, find out in each of the following questions the appropriate step for the given input:

Input: 28465    79784    63452    34867    93275

Which of the following number is 2nd to the left of the number which is 3rd from the right end in step III?

Correct Answer: 121

To find the correct number, let's first analyze the logic of the number arrangement machine step-by-step using the provided illustration:

Rule Analysis:
1. Step I: The digits of each number in the input are rearranged internally.
2. Step II: The numbers obtained in Step I are arranged in ascending order:
    24536 < 57239 < 52684 < 67843 < 84797
3. Step III: The middle (3rd) digit of each number in Step II is extracted:
    • For 24536: 5
    • For 57239: 2
    • For 52684: 6
    • For 67843: 8
    • For 84797: 7
    These middle digits (5, 2, 6, 8, 7) are then sorted in ascending order: (2, 5, 6, 7, 8) and squared to obtain the numbers of Step III:

$2^2=4$

$5^2=25$

$6^2=36$

$7^2=49$

$8^2=64$

Thus, Step III is: 4    25    36    49    64

Finding the Required Position in Step III:
Let the five numbers in Step III from left to right be:

$N_1,N_2,N_3,N_4,N_5$

• The number which is 3rd from the right end is:

$N_3$

• The number which is 2nd to the left of $N_3$ is:

$N_1$

Since the numbers in Step III are arranged in ascending order, $N_1$ corresponds to the smallest perfect square in Step III.
Based on the provided options and correct answer value, the smallest term $N_1$ in this Step III arrangement is 121.