Question
Which of the following numbers is divisible by 11?
This question was previously asked in
RRB ALP 2025 CBT 2 Wiremen Question Paper (28-Jul-2026) (Shift 2)
The correct answer is
232144
Divisibility by 11 Rule Explained
To determine if a number is divisible by 11, apply the alternating sum of digits rule:
- Sum the digits occupying the odd positions (1st, 3rd, 5th, etc., counting from the right).
- Sum the digits occupying the even positions (2nd, 4th, 6th, etc., counting from the right).
- Calculate the absolute difference between these two sums.
- If the difference is 0 or any multiple of 11, the original number is divisible by 11.
Applying Divisibility Test to Numbers
We will test each option using the divisibility rule for 11:
| Number | Sum of Odd Place Digits | Sum of Even Place Digits | Difference (Odd Sum - Even Sum) | Divisible by 11? |
|---|---|---|---|---|
| 322431 | \(1 + 4 + 2 = 7\) | \(3 + 2 + 3 = 8\) | \(7 - 8 = -1\) | No |
| 432321 | \(1 + 3 + 3 = 7\) | \(2 + 2 + 4 = 8\) | \(7 - 8 = -1\) | No |
| 232144 | \(4 + 1 + 3 = 8\) | \(4 + 2 + 2 = 8\) | \(8 - 8 = 0\) | Yes |
| 231243 | \(3 + 2 + 3 = 8\) | \(4 + 1 + 2 = 7\) | \(8 - 7 = 1\) | No |
Conclusion:
The number 232144 yields a difference of 0 when applying the divisibility rule for 11 (\(8 - 8 = 0\)). Therefore, 232144 is divisible by 11.
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