Direction : A number arrangement machine when given an input line of numbers…
2021
Direction : A number arrangement machine when given an input line of numbers rearranges them following a particular rule in each step. The following is an illustration of input and rearrangement:
Input:84629 57426 76932 27483 49853 62434
Step I:273 84629 57426 76932 49853 62434
Step II: 53 273 84629 57426 76932 62434
Step III:572 53 273 84629 76932 62434
Step IV:23 572 53 273 84629 76932
Step V:732 23 572 53 273 84629
Step VI:2 732 23 572 53 273
Step VI is the last step of the given arrangement. Based on the given logic, rearrange the given input.
Input: 63825 49857 38679 72548 45328 95763
If all the numbers in step VI are arranged in ascending order from left end, then which of the following number will become 3rd from right end?
- A.
57
- B.
573
- C.
532
- D.
325
- E.
None of these
Attempted by 1 students.
Show answer & explanation
Correct answer: C
Concept: In a number-arrangement machine, first decode the transformation rule from the worked illustration, then replay that exact rule on the new input. Keep two things separate: (a) the order in which the machine picks up numbers, and (b) what it does to each picked number. The final step holds the fully transformed collection, and any further instruction (here, re-sorting) is applied only to that collection.
Decoding the rule: Compare each original number with the short number that appears at the left end when it is processed:
27483 becomes 273, 49853 becomes 53, 57426 becomes 572, 62434 becomes 23, 76932 becomes 732, 84629 becomes 2.
In every case only the prime digits 2, 3, 5, 7 are kept, in their original left-to-right order; the non-prime digits (0,1,4,6,8,9) are dropped.
The numbers are processed one per step in ascending order of their first digit, and each transformed number is placed at the far left.
Application to the new input 63825, 49857, 38679, 72548, 45328, 95763 — keep only the prime digits of each:
63825 keeps 3,2,5 = 325
49857 keeps 5,7 = 57
38679 keeps 3,7 = 37
72548 keeps 7,2,5 = 725
45328 keeps 5,3,2 = 532
95763 keeps 5,7,3 = 573
So the final step is made up of exactly these six transformed values (their display order does not matter here, since the next instruction re-sorts them): 37, 57, 325, 532, 573, 725 once written out as a set.
Final instruction — arrange the final step in ascending order from the left end: 37, 57, 325, 532, 573, 725. Reading from the right end gives 725, then 573, then 532, so the number that becomes 3rd from the right end is 532.
Cross-check: The three-digit values 325, 532, 573, 725 are all larger than the two-digit values 37 and 57, so the four three-digit numbers occupy the right side; in ascending order 325 < 532 < 573 < 725, which places 532 third when counting in from the right end and confirms the result.