When a line of words and numbers is fed into a machine, the machine rearranges it step by step following a particular rule. An illustration of an input and its rearrangement is given below.
Input: vale hill cave 14 reef 49 16 45
Step I: cave vale hill 14 reef 49 16 45
Step II: cave 14 vale hill reef 49 16 45
Step III: cave 14 hill vale reef 49 16 45
Step IV: cave 14 hill 16 vale reef 49 45
Step V: cave 14 hill 16 reef vale 49 45
Step VI: cave 14 hill 16 reef 45 vale 49
Step VI is the last step of this input.
Step II of another input is: bell 25 95 lute 45 drum horn 88
Following the same rule, which of the following will be Step VI for that input?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → bell 25 drum 45 horn 88 95 lute
Compare each step of the illustration with the one before it. Words and numbers are placed by turns from the left end: in Steps I, III, V, ... the word that comes first in dictionary order among the words left, and in Steps II, IV, VI, ... the smallest of the numbers left, moves to the next place; the others keep their order.
Step I: ‘cave’ comes first in dictionary order, so it moves to the first place from the left
Step II: 14 is the smallest of the numbers left, so it moves to the second place from the left
Step III: ‘hill’ comes first in dictionary order, so it moves to the third place from the left
Step IV: 16 is the smallest of the numbers left, so it moves to the fourth place from the left
Step V: ‘reef’ comes first in dictionary order, so it moves to the fifth place from the left
Step VI: 45 is the smallest of the numbers left, so it moves to the sixth place from the left
After Step VI words and numbers come by turns, the words in dictionary order and the numbers from the smallest to the largest, so the arrangement is complete.
In Step II the first two elements, bell 25, are already in place. Continue from Step II with the same rule.
Step III: ‘drum’ comes first in dictionary order, so it moves to the third place from the left, giving bell 25 drum 95 lute 45 horn 88
Step IV: 45 is the smallest of the numbers left, so it moves to the fourth place from the left, giving bell 25 drum 45 95 lute horn 88
Step V: ‘horn’ comes first in dictionary order, so it moves to the fifth place from the left, giving bell 25 drum 45 horn 95 lute 88
Step VI: 88 is the smallest of the numbers left, so it moves to the sixth place from the left, giving bell 25 drum 45 horn 88 95 lute
So Step VI is bell 25 drum 45 horn 88 95 lute.
Why the other options are incorrect
Option (1) bell 25 drum 45 horn 95 lute 88 — Incorrect. This is Step V; in Step VI the number 88 must also be placed.
Option (2) bell 25 drum 45 horn 88 lute 95 — Incorrect. This is Step VII, the last step, where ‘lute’ has also been placed.
Option (4) bell 25 drum 45 horn lute 88 95 — Incorrect. Here ‘lute’ is placed in Step VI; Step VI is an even step, so a number (88) is placed in it.