A number arrangement machine, when given an input line of numbers, rearranges them step by step following a particular rule. An illustration of an input and its rearrangement is given below.
Input: 87 65 93 11 82 54 60
Step I: 60 87 65 93 11 82 54
Step II: 60 11 87 65 93 82 54
Step III: 60 11 82 87 65 93 54
Step IV: 60 11 82 93 87 65 54
Step V: 60 11 82 93 54 87 65
Step VI: 60 11 82 93 54 65 87
Step VI is the last step of this input.
Input: 49 61 94 28 17 32 96
Following the same rule, which step of this input will be 61 32 94 96 49 28 17?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Step IV
Compare each step of the illustration with the one before it. In each step, the number with the smallest unit digit among the numbers not yet arranged moves to the next place from the left end, and all the other numbers keep their order.
Step I: 60 has unit digit 0, the smallest among the numbers left, so it moves to the first place from the left
Step II: 11 has unit digit 1, the smallest among the numbers left, so it moves to the second place from the left
Step III: 82 has unit digit 2, the smallest among the numbers left, so it moves to the third place from the left
Step IV: 93 has unit digit 3, the smallest among the numbers left, so it moves to the fourth place from the left
Step V: 54 has unit digit 4, the smallest among the numbers left, so it moves to the fifth place from the left
Step VI: 65 has unit digit 5, the smallest among the numbers left, so it moves to the sixth place from the left
After Step VI every one of the numbers is in its final place, so the arrangement is complete.
Apply the same rule to the input 49 61 94 28 17 32 96.
Step I: 61 has unit digit 1, the smallest among the numbers left, so it moves to the first place from the left, giving 61 49 94 28 17 32 96
Step II: 32 has unit digit 2, the smallest among the numbers left, so it moves to the second place from the left, giving 61 32 49 94 28 17 96
Step III: 94 has unit digit 4, the smallest among the numbers left, so it moves to the third place from the left, giving 61 32 94 49 28 17 96
Step IV: 96 has unit digit 6, the smallest among the numbers left, so it moves to the fourth place from the left, giving 61 32 94 96 49 28 17
So the arrangement 61 32 94 96 49 28 17 is Step IV.
Why the other options are incorrect
Option (1) Step II — Incorrect. Step II is 61 32 49 94 28 17 96.
Option (2) Step III — Incorrect. Step III is 61 32 94 49 28 17 96.
Option (4) Step V — Incorrect. Step V is 61 32 94 96 17 49 28.