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: whale 14 19 tulip crab 74 cotton 25 timber 68
Step I: 74 whale 14 19 tulip crab cotton 25 timber 68
Step II: 74 cotton whale 14 19 tulip crab 25 timber 68
Step III: 74 cotton 68 whale 14 19 tulip crab 25 timber
Step IV: 74 cotton 68 crab whale 14 19 tulip 25 timber
Step V: 74 cotton 68 crab 25 whale 14 19 tulip timber
Step VI: 74 cotton 68 crab 25 timber whale 14 19 tulip
Step VII: 74 cotton 68 crab 25 timber 19 whale 14 tulip
Step VIII: 74 cotton 68 crab 25 timber 19 tulip whale 14
Step IX: 74 cotton 68 crab 25 timber 19 tulip 14 whale
Step IX is the last step of this input.
Input: hockey fox 41 18 cricket 40 atlas falcon 77 62
Following the same rule, in Step V for this input, which element will be third to the right of ‘hockey’?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 40
Compare each step of the illustration with the one before it. The machine places a number and a word by turns from the left end. In Steps I, III, V, ... the largest of the numbers left moves to the next place from the left; in Steps II, IV, VI, ... the word that comes first in dictionary order among the words left moves to the next place from the left. The others keep their order.
Step I: 74 is the largest of the numbers left, so it moves to the first place from the left
Step II: ‘cotton’ comes first in dictionary order among the words left, so it moves to the second place from the left
Step III: 68 is the largest of the numbers left, so it moves to the third place from the left
Step IV: ‘crab’ comes first in dictionary order among the words left, so it moves to the fourth place from the left
Step V: 25 is the largest of the numbers left, so it moves to the fifth place from the left
Step VI: ‘timber’ comes first in dictionary order among the words left, so it moves to the sixth place from the left
Step VII: 19 is the largest of the numbers left, so it moves to the seventh place from the left
Step VIII: ‘tulip’ comes first in dictionary order among the words left, so it moves to the eighth place from the left
Step IX: 14 is the largest of the numbers left, so it moves to the ninth place from the left
After Step IX the numbers (from the largest to the smallest) and the words (in dictionary order) stand by turns, so the arrangement is complete.
Apply the same rule to the input hockey fox 41 18 cricket 40 atlas falcon 77 62.
Step I: 77 is the largest of the numbers left, so it moves to the first place from the left, giving 77 hockey fox 41 18 cricket 40 atlas falcon 62
Step II: ‘atlas’ comes first in dictionary order among the words left, so it moves to the second place from the left, giving 77 atlas hockey fox 41 18 cricket 40 falcon 62
Step III: 62 is the largest of the numbers left, so it moves to the third place from the left, giving 77 atlas 62 hockey fox 41 18 cricket 40 falcon
Step IV: ‘cricket’ comes first in dictionary order among the words left, so it moves to the fourth place from the left, giving 77 atlas 62 cricket hockey fox 41 18 40 falcon
Step V: 41 is the largest of the numbers left, so it moves to the fifth place from the left, giving 77 atlas 62 cricket 41 hockey fox 18 40 falcon
In Step V, 77 atlas 62 cricket 41 hockey fox 18 40 falcon, count to the right of ‘hockey’: fox (first), 18 (second), 40 (third).
So the element third to the right of ‘hockey’ is 40.