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?
Correct Answer :
532
Solution :
The correct answer is 532.
Logic and Pattern Analysis:
By analyzing the given illustration step-by-step, we can identify two main rules applied in each step:
1. Selection Rule: In each step, the smallest remaining original number from the input is selected in ascending order (from smallest to largest):
- Step I selects the 1st smallest number.
- Step II selects the 2nd smallest number.
- Step III selects the 3rd smallest number, and so on.
2. Transformation Rule: The selected number is transformed by keeping only its prime digits (2, 3, 5, 7) in their original relative positions, while dropping all non-prime digits (0, 1, 4, 6, 8, 9). The transformed number is then placed at the extreme left end of the line.
Illustration Verification:
Let's verify this logic on the given example numbers: 84629, 57426, 76932, 27483, 49853, 62434.
- Smallest number: 27483 ⇒ Prime digits: 2, 7, 3 ⇒ Transformed to 273 (Step I)
- Next smallest: 49853 ⇒ Prime digits: 5, 3 ⇒ Transformed to 53 (Step II)
- Next smallest: 57426 ⇒ Prime digits: 5, 7, 2 ⇒ Transformed to 572 (Step III)
- Next smallest: 62434 ⇒ Prime digits: 2, 3 ⇒ Transformed to 23 (Step IV)
- Next smallest: 76932 ⇒ Prime digits: 7, 3, 2 ⇒ Transformed to 732 (Step V)
- Largest number: 84629 ⇒ Prime digits: 2 ⇒ Transformed to 2 (Step VI)
Applying the Pattern to the Target Input:
Given Input: 63825, 49857, 38679, 72548, 45328, 95763
Let's order the original numbers from smallest to largest:
1. 38679
2. 45328
3. 49857
4. 63825
5. 72548
6. 95763
Now, let's determine the steps for the given input:
Step I: Pick 38679 ⇒ Prime digits: 3, 7 ⇒ 37
Line: 37, 63825, 49857, 72548, 45328, 95763
Step II: Pick 45328 ⇒ Prime digits: 5, 3, 2 ⇒ 532
Line: 532, 37, 63825, 49857, 72548, 95763
Step III: Pick 49857 ⇒ Prime digits: 5, 7 ⇒ 57
Line: 57, 532, 37, 63825, 72548, 95763
Step IV: Pick 63825 ⇒ Prime digits: 3, 2, 5 ⇒ 325
Line: 325, 57, 532, 37, 72548, 95763
Step V: Pick 72548 ⇒ Prime digits: 7, 2, 5 ⇒ 725
Line: 725, 325, 57, 532, 37, 95763
Step VI: Pick 95763 ⇒ Prime digits: 5, 7, 3 ⇒ 573
Line: 573, 725, 325, 57, 532, 37
Final Step Analysis:
The numbers present in Step VI are: 573, 725, 325, 57, 532, 37.
Arranging all numbers in Step VI in ascending order (from left to right):
37, 57, 325, 532, 573, 725
Counting from the right end:
- 1st from right: 725
- 2nd from right: 573
- 3rd from right: 532
Therefore, the number that becomes 3rd from the right end is 532.
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