A word and number arrangement machine was given an input line of words and…
2025
A word and number arrangement machine was given an input line of words and numbers rearranges them following a particular rule in each step. The following is an illustration of input and rearrangement.
Input : Various 26 Target 21 For 88 Host 54 Taste 46
Step I : For Various 26 Target 21 88 Host 54 Taste 46
Step II : Host For Various 26 Target 88 54 Taste 46 21
Step III : Taste Host For Various 26 Target 54 46 21 88
Step IV : Target Taste Host For Various 54 46 21 88 26
Step V : Various Target Taste Host For 46 21 88 26 54
Step V is the last step. Find the various steps and final output for the input given below :
Input : Strike 82 Reference 25 Depends 38 Of 53 Wind 36
Which of the following elements is second to the left of third element from right end in Step III ?
- A.
Depends
- B.
Wind
- C.
Of
- D.
53
Show answer & explanation
Correct answer: D
Concept
In a word-and-number arrangement machine, each step moves exactly one word to one end and one number to the other end, following two fixed ordering rules. You first decode both rules from the given illustration, then replay them on the new input.
Words are ordered by their length (number of letters): the shortest word goes to the left end first, then the next shortest, and so on.
Numbers are ordered by their digital root — repeatedly add a number's digits until a single digit remains (for example 88 gives 8 + 8 = 16, then 1 + 6 = 7). The number with the smallest digital root goes to the right end first, then the next smallest, and so on.
Applying the rule
New input: Strike 82 Reference 25 Depends 38 Of 53 Wind 36.
Word order by length: Of (2) is shortest, then Wind (4), Strike (6), Depends (7), Reference (9).
Number order by digital root: 82 gives 1, 38 gives 2, 25 gives 7, 53 gives 8, 36 gives 9.
Of Strike Reference 25 Depends 38 53 Wind 36 82
Wind Of Strike Reference 25 Depends 53 36 82 38
Strike Wind Of Reference Depends 53 36 82 38 25
Depends Strike Wind Of Reference 36 82 38 25 53
Reference Depends Strike Wind Of 82 38 25 53 36
Locating the required element
Take Step III: Strike Wind Of Reference Depends 53 36 82 38 25. Counting from the right end, 25 is the 1st, 38 is the 2nd and 82 is the 3rd, so the third element from the right end is 82.
Now move two places to the left of 82: the first place to its left is 36 and the second place to its left is 53. So the required element is 53.
Cross-check: these same two rules reproduce the illustration exactly — For (3), Host (4), Taste (5), Target (6), Various (7) to the left, and 46 (root 1), 21 (root 3), 88 (root 7), 26 (root 8), 54 (root 9) to the right — which confirms the decoding.