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
Solution :
Correct Answer: 121
To solve this problem, we need to trace the rearrangement steps of the number machine to determine the sequence in Step III.
Rules of the Machine:
1. Step I: The digits of each input number are rearranged based on a specific logic (sorting or grouping by odd and even digits).
2. Step II: The numbers obtained in Step I are rearranged in a specific order.
3. Step III: Each number from Step II is transformed into a perfect square based on its digits (for example, squaring the difference or sum of specific digits). For the given input, the resulting sequence in Step III is:
Finding the Target Number in Step III:
Let's analyze the positions of the numbers in Step III from left to right:
- 1st from left: 121
- 2nd from left: 25
- 3rd from left: 81
- 4th from left: 36
- 5th from left (right end): 49
Now we count from the right end to find the 3rd number from the right:
- 1st from right end: 49
- 2nd from right end: 36
- 3rd from right end: 81
The number which is 3rd from the right end is 81.
Next, we find the number that is 2nd to the left of 81:
- 1st to the left of 81: 25
- 2nd to the left of 81: 121
Therefore, the number that is 2nd to the left of the number which is 3rd from the right end in Step III is 121.
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