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Which number is divisible by 11?
1234
1331
2468
9876
1331
Calculate the alternating sum of digits starting from the right (or left). If the result is 0 or a multiple of 11, the number is divisible by 11.
A set of four-digit numbers: 1234, 1331, 2468, 9876.
тИг(Sum┬аof┬аodd-position┬аdigits)тИТ(Sum┬аof┬аeven-position┬аdigits)тИг=0┬аor┬а11k
Calculate the alternating sum of digits starting from the right (or left). If the result is 0 or a multiple of 11, the number is divisible by 11.
Students often start alternating from the wrong end or subtract incorrectly; remember the result must be 0 or a multiple of 11, not just any small number.
Apply Rule to 1234
Sum of odd positions (4+2=6), sum of even positions (3+1=4). The difference is 6-4=2, which is not divisible by 11.
тИг6тИТ4тИг=2
Apply Rule to 1331
Sum of odd positions (1+3=4), sum of even positions (3+1=4). The difference is 4-4=0, which satisfies the divisibility rule for 11.
тИг4тИТ4тИг=0
Apply Rule to 2468
Sum of odd positions (8+4=12), sum of even positions (6+2=8). The difference is 12-8=4, not divisible by 11.
тИг12тИТ8тИг=4
Apply Rule to 9876
Sum of odd positions (6+8=14), sum of even positions (7+9=16). The difference is |14-16|=2, not divisible by 11.
тИг14тИТ16тИг=2
B is correct because the alternating sum of digits for 1331 is 0, satisfying the divisibility criterion for 11.
The rule for 11 is highly efficient for verifying large prime factorizations in number theory and is frequently tested in RRB exams for quick verification.
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