Directions: A word/number arrangement machine is given an input line of words…

2024

Directions: A word/number arrangement machine is given an input line of words and numbers; it arranges them following a particular rule in each step. The following is an illustration of input and its arrangement:

Input: triangle 45 38 galaxy 93 puzzle 27 velocity rhythm 84
Step I: 88 triangle 45 38 puzzle 27 velocity rhythm 84 aaglxy
Step II: 87 88 triangle 45 38 27 velocity rhythm aaglxy eulpzz
Step III: 40 87 88 triangle 38 27 velocity aaglxy eulpzz hhmrty
Step IV: 41 40 87 88 27 velocity aaglxy eulpzz hhmrty aeiglnrt
Step V: 22 41 40 87 88 aaglxy eulpzz hhmrty aeiglnrt eiocltvy
Based on the above example, rearrange the below input:
Input: shadow 74 19 magnet 52 forest 68 bridge whistle 31

Which element is 5th to the right of second least number in step V?

  1. A.

    eibdgr

  2. B.

    31

  3. C.

    eofrst

  4. D.

    aegmnt

  5. E.

    None of these

Attempted by 1 students.

Show answer & explanation

Correct answer: C

Concept

In an input–output arrangement machine, every step rearranges the line using one fixed, hidden rule. Decode the rule once from the worked example, then apply the very same rule mechanically to the new input. Here two independent operations run together in each step: one number is shifted to the LEFT end and one word is shifted to the RIGHT end.

The decoded rule

  1. Numbers go to the LEFT, largest first. The largest remaining number moves to the front each step; numbers are picked in descending order: 74, 68, 52, 31, 19.

  2. The number is changed before it lands: the 1st, 3rd, 5th number picked is reduced by 5; the 2nd and 4th picked is increased by 3. So 74−5=69, 68+3=71, 52−5=47, 31+3=34, 19−5=14.

  3. Words go to the RIGHT, in alphabetical order: bridge, forest, magnet, shadow, whistle.

  4. Each word is rewritten by placing its vowels in alphabetical order first, then its consonants in alphabetical order. Example: forest → vowels e, o then consonants f, r, s, t → "eofrst".

Applying it to the input

Input: shadow 74 19 magnet 52 forest 68 bridge whistle 31

  1. Step I: 69 shadow 19 magnet 52 forest 68 whistle 31 eibdgr

  2. Step II: 71 69 shadow 19 magnet 52 whistle 31 eibdgr eofrst

  3. Step III: 47 71 69 shadow 19 whistle 31 eibdgr eofrst aegmnt

  4. Step IV: 34 47 71 69 19 whistle eibdgr eofrst aegmnt aodhsw

  5. Step V: 14 34 47 71 69 eibdgr eofrst aegmnt aodhsw eihlstw

Reading the answer

In Step V the five numbers are 14, 34, 47, 71, 69. The least is 14 and the second least is 34. Counting five positions to the right of 34 (47, 71, 69, eibdgr, eofrst) lands on "eofrst". So the required element is eofrst.

Cross-check

Re-running the same rule on the original illustration reproduces all five of its given steps exactly (93−5=88, 84+3=87, …; galaxy→aaglxy, puzzle→eulpzz, …), which confirms the decoded rule is correct.

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