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
What is sum of all the odd numbers in step II?
- A.
110
- B.
147
- C.
128
- D.
117
- E.
198
Attempted by 1 students.
Show answer & explanation
Correct answer: E
Concept
In an input-output "machine" question, first decode the fixed rule from the worked example, then apply that exact rule to the new input. Read the per-step rule by comparing consecutive steps: identify (a) the order in which items are picked, and (b) any value transformation applied to a picked item.
The rule from the example
In every step the largest remaining number is moved to the far-left after being transformed, while one word is sent to the right. The number transformation is parity-based: an odd number is reduced by 5, and an even number is increased by 3.
Verify on the example: 93 (odd) becomes 88, 84 (even) becomes 87, 45 (odd) becomes 40, 38 (even) becomes 41, 27 (odd) becomes 22. Every move fits, and numbers are processed in descending order.
Apply to the new input
New input numbers: 74, 19, 52, 68, 31. Descending order: 74, 68, 52, 31, 19.
Step I picks the largest, 74 (even), and transforms it to 74 + 3 = 77 at the far left. Numbers still in the middle: 19, 52, 68, 31.
Step II picks the next largest, 68 (even), and transforms it to 68 + 3 = 71, placed to the far left of 77. The numbers still untransformed in the middle are 19, 52, 31.
Therefore the numbers present in Step II are 77, 71, 19, 52 and 31.
Odd numbers in Step II: 77, 71, 19 and 31. Sum = 77 + 71 + 19 + 31 = 198.
Cross-check
The example's Step II literally reads "87 88 triangle 45 38 27 ...": it contains both the transformed left numbers (87, 88) and the not-yet-processed middle numbers (45, 38, 27). So a step genuinely contains both kinds of numbers. The same reading on the new input gives the odd-number set {77, 71, 19, 31} and the sum 198.