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: millet 66 61 garlic 27 12 compass globe
Step I: compass millet 66 61 garlic 27 globe 12
Step II: compass garlic millet 66 61 globe 27 12
Step III: compass garlic globe millet 66 61 27 12
Step III is the last step of this input.
Input: 60 rabbit walnut 29 knife atlas 56 88
Following the same rule, which of the following will be Step II for this input?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → atlas knife 60 rabbit walnut 88 56 29
Compare each step of the illustration with the one before it. In each step, the word that comes first in dictionary order among the words left moves to the next place from the left end, and the smallest of the numbers left moves to the next place from the right end; the others keep their order.
Step I: ‘compass’ (first in dictionary order) moves to the first place from the left, and 12 (the smallest number left) moves to the first place from the right
Step II: ‘garlic’ (first in dictionary order) moves to the second place from the left, and 27 (the smallest number left) moves to the second place from the right
Step III: ‘globe’ (first in dictionary order) moves to the third place from the left, and 61 (the smallest number left) moves to the third place from the right
After Step III the words stand in dictionary order on the left and the numbers from the largest to the smallest on the right, so the arrangement is complete.
Apply the same rule to the input 60 rabbit walnut 29 knife atlas 56 88.
Step I: ‘atlas’ (first in dictionary order) moves to the first place from the left, and 29 (the smallest number left) moves to the first place from the right, giving atlas 60 rabbit walnut knife 56 88 29
Step II: ‘knife’ (first in dictionary order) moves to the second place from the left, and 56 (the smallest number left) moves to the second place from the right, giving atlas knife 60 rabbit walnut 88 56 29
So Step II is atlas knife 60 rabbit walnut 88 56 29.
Why the other options are incorrect
Option (1) atlas 60 rabbit walnut knife 88 56 29 — Incorrect. Only 56 has moved; in the same step ‘knife’, first in dictionary order, must go to the second place from the left.
Option (2) atlas 60 rabbit walnut knife 56 88 29 — Incorrect. This is Step I; in Step II ‘knife’ and 56 must also move.
Option (3) atlas knife 60 rabbit walnut 56 88 29 — Incorrect. Only ‘knife’ has moved; in the same step 56, the smallest number left, must go to the second place from the right.