Question

A number arrangement machine, when given a particular input, rearranges it following a particular rule. The following is an illustration of the input and the stages of arrangement.
Input: 245, 316, 436, 519, 868, 710, 689
Step I: 710, 316, 436, 519, 868, 245, 689
Step II: 710, 316, 245, 519, 868, 436, 689
Step III: 710, 316, 245, 436, 868, 519, 689
Step IV: 710, 316, 245, 436, 519, 868, 689
Step IV is the last step of the rearrangement of the above input.
How many steps are required to get the final output form the following input?
Input: 544, 653, 325, 688, 461, 231, 857

• A. 4
• B. 5
• C. 6
• D. 3
• E. 2

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The machine rearranges numbers based on a specific logic. We must decode the logic from the example and apply it to a new input.
Step 2: Detailed Explanation:

Analyzing Logic: Look at the final Step IV: 710, 316, 245, 436, 519, 868, 689.
Let's check the sum of digits:
- 245: 2+4+5=11
- 316: 3+1+6=10
- 436: 4+3+6=13
- 519: 5+1+9=15
- 868: 8+6+8=22
- 710: 7+1+0=8
- 689: 6+8+9=23
Ordered sums: 8, 10, 11, 13, 15, 22, 23.
The rule is to sort the numbers in ascending order of their digit sums.

New Input Logic: Input: 544 (13), 653 (14), 325 (10), 688 (22), 461 (11), 231 (6), 857 (20).
Target order: 231 (6), 325 (10), 461 (11), 544 (13), 653 (14), 857 (20), 688 (22).

Step by Step Arrangement:
- Input: 544, 653, 325, 688, 461, 231, 857
- Step I: 231, 653, 325, 688, 461, 544, 857 (Bring 231 to front)
- Step II: 231, 325, 653, 688, 461, 544, 857 (Bring 325 to 2nd)
- Step III: 231, 325, 461, 688, 653, 544, 857 (Bring 461 to 3rd)
- Step IV: 231, 325, 461, 544, 653, 688, 857 (Bring 544 to 4th)
- Step V: 231, 325, 461, 544, 653, 857, 688 (Bring 857 to 6th)

Step 3: Final Answer:
It takes 5 steps to reach the final arrangement. Option (B) is correct.