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A number arrangement machine, when given a particular input, rearranges it following a particular rule. Illustrations of the input and the steps of arrangement is given below.
Input: 245, 316, 436, 519, 868, 710, 689
Step 1: 710, 316, 436, 519, 868, 245, 689
Step 2: 710, 316, 245, 519, 868, 436, 689
Step 3: 710, 316, 245, 436, 868, 519, 689
Step 4: 710, 316, 245, 436, 519, 868, 689
Step 4 is the last step for the given input
How many steps will be required to get the final output from the following input?
Input: 544, 653, 325, 688, 461, 231, 857
The machine arranges the numbers in the increasing order of the sum of the digits on the number.
Input: 245 (11), 316 (10), 436 (13), 519 (15), 868 (22), 710 (8), 689 (23).
The number in the bracket indicates the sum of digits of the given number.
Step 1: 710 (8), 316 (10), 436 (13), 519 (15), 868 (22), 245 (11), 689 (23).
∴ The machine has swapped 710 (8) with 245 (11).
Step 2: 710 (8), 316 (10), 245 (11), 519 (15), 868 (22), 436 (13), 689 (23).
Thus it has swapped 436 (13) with 245 (11).
Step 3: 710 (8), 316 (10), 245 (11), 436 (13), 868 (22), 519 (15), 689 (23).
Thus it has swapped 436 (13) with 519 (15).
Step 4: 710 (8), 316 (10), 245 (11), 436 (13), 519 (15), 868 (22), 689 (23).
Thus it has swapped 519 (15) with 868 (22).
Given input: 544(14), 653(14), 325(10), 688(22), 461(11), 231(6), 857(20)
Step 1: 231, 653, 325, 688, 461, 544, 857
Step 2: 231, 325, 653, 688, 461, 544, 857
Step 3: 231, 325, 461, 688, 653, 544, 857
Step 4: 231, 325, 461, 544, 653, 688, 857
Step 5: 231, 325, 461, 544, 653, 857, 688
Thus, the correct option is B.
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