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
Find the square of the 2nd highest number in Step III.
Answer: E. None of these — ConceptIn an input-output 'arrangement machine' problem, exactly one rule generates every step. To solve any query you must first decode that rule from the…
- A.
3844
- B.
3025
- C.
2809
- D.
5041
- E.
None of these
Attempted by 2 students.
Show answer & explanation
Correct answer: E
Concept
In an input-output 'arrangement machine' problem, exactly one rule generates every step. To solve any query you must first decode that rule from the worked illustration: identify (i) the order in which items are picked, (ii) how each picked number/word is transformed, and (iii) where it is placed. Once the rule is fixed, you replay it on the new input and simply read off the requested quantity.
Decoding the rule from the illustration
Track the numbers only. In each step one number leaves the body and a transformed value appears at the front. Matching front values to the number that disappears:
93 → 88 (the largest is picked first; −5)
84 → 87(next largest; +3)
45 → 40(next; −5)
38 → 41(next; +3)
27 → 22(smallest; −5)
So the rule for numbers is: pick numbers in descending order, one per step, move the transformed value to the front, and apply the alternating shift −5, +3, −5, +3, −5 by pick-position. (The words are simultaneously transformed and sent to the end, but they play no part in this number-only query.)
Applying the rule to the new input
New input numbers: 74, 19, 52, 68, 31. In descending order they are 74, 68, 52, 31, 19. Apply the position shifts:
Pick 1: 74 − 5 = 69
Pick 2: 68 + 3 = 71
Pick 3: 52 − 5 = 47
Pick 4: 31 + 3 = 34
Pick 5: 19 − 5 = 14
By Step III, three numbers have been moved to the front (69, 71, 47) and two original numbers are still untouched in the body (31, 19). Therefore the numbers present in Step III are: 71, 69, 47, 31, 19.
Highest in Step III = 71; the 2nd highest = 69.
Result and cross-check
Square of the 2nd highest = 69×69 = 4761.
4761 does not equal any of 3844 (=622), 3025 (=552), 2809 (=532) or 5041 (=712). Note 5041 = 712 is the square of the HIGHEST number in Step III, not the 2nd highest, so it is a trap. Cross-check the rule on the illustration's own Step III (40, 87, 88, 38, 27): the two largest are 88 and 87, consistent with descending picks plus the −5/+3 shifts. Hence the correct choice is 'None of these'.