Question

If in the number 546839271, 1 is added to first, third, fifth, seventh and ninth digit and 1 is subtracted from the second, fourth, sixth and eighth digits, then all digits are arranged in descending order from left to right. Which of the following digit is 4th from the right end?

• A. 7
• B. 6
• C. 3
• D. 4
• E. 5

Hint:

To avoid confusion with positions, write the numbers 1-9 directly above the digits before starting. When sorting in descending order, the "4th from the right" in a 9-digit set is also the "6th from the left."

Answer 1

Answer: (E)

Concept:
This problem requires a step-by-step numerical transformation followed by a re-sorting of the digits. We must be careful to apply the operations to the correct positional indices.

Step 1: Apply addition and subtraction rules to the number 546839271.
Original Number: 5 4 6 8 3 9 2 7 1
Positions: 1 2 3 4 5 6 7 8 9
• Odd positions (1, 3, 5, 7, 9) $+ 1$:
5+1=6, 6+1=7, 3+1=4, 2+1=3, 1+1=2.
• Even positions (2, 4, 6, 8) $- 1$:
4-1=3, 8-1=7, 9-1=8, 7-1=6. The transformed digits are: 6, 3, 7, 7, 4, 8, 3, 6, 2.


Step 2: Arrange the digits in descending order (largest to smallest).
The digits are: 8, 7, 7, 6, 6, 4, 3, 3, 2.


Step 3: Find the 4th digit from the right end.
Counting from the right:
• 1st from right: 2
• 2nd from right: 3
• 3rd from right: 3
• 4th from right: 4 --- Wait, re-checking... Let's re-sort: 8 (1st left), 7 (2nd), 7 (3rd), 6 (4th), 6 (5th), 4 (6th), 3 (7th), 3 (8th), 2 (9th).
Counting from right end: 2 (1st), 3 (2nd), 3 (3rd), 4 (4th). Self-Correction: If we look at the provided options, let's re-verify the transformed digits: (5+1=6), (4-1=3), (6+1=7), (8-1=7), (3+1=4), (9-1=8), (2+1=3), (7-1=6), (1+1=2). Sorted Descending: 8, 7, 7, 6, 6, 4, 3, 3, 2. The 4th from the right is indeed 4.