Each of the digits in the number 6543127 is arranged in ascending order from…
2026
Each of the digits in the number 6543127 is arranged in ascending order from left to right. What will be the sum of the digits which are second from the left and second from the right in the new number thus formed?
Answer: C. 8 — Concept: Rearranging the digits of a number moves them to new places but never changes the digits themselves. In a number of n digits, the place counted k-th…
- A.
5
- B.
3
- C.
8
- D.
7
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Show answer & explanation
Correct answer: C
Concept: Rearranging the digits of a number moves them to new places but never changes the digits themselves. In a number of n digits, the place counted k-th from the right is the very same place as the one counted (n − k + 1)-th from the left, so any counting from an end must be carried out on the rearranged number and not on the original one.
Application:
The number 6543127 is made of the digits 6, 5, 4, 3, 1, 2 and 7 — seven digits in all, so n = 7.
Written in ascending order, smallest digit first, these same digits form the new number 1234567.
Counting two places from the left in 1234567 reaches the digit 2.
Counting two places from the right means the place 7 − 2 + 1 = 6 from the left, and the digit standing there is 6.
The sum asked for is therefore 2 + 6 = 8.
Cross-check: The table below pairs every place of 1234567 with its distance from each end.
Place from the left | Place from the right | Digit |
|---|---|---|
1 | 7 | 1 |
2 | 6 | 2 |
3 | 5 | 3 |
4 | 4 | 4 |
5 | 3 | 5 |
6 | 2 | 6 |
7 | 1 | 7 |
Reading 1234567 in reverse gives 7654321, whose second digit is again 6, which confirms the place formula. The rearrangement also keeps the digits unchanged: 6 + 5 + 4 + 3 + 1 + 2 + 7 = 28 and 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28.