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Which of the following numbers is divisible by 11?
1234
1331
1442
1553
1331
Calculate the alternating sum of digits (from right to left). If the result is 0 or divisible by 11, the number is divisible by 11.
A set of four numbers: 1234, 1331, 1442, and 1553.
(Sumodd┬аpositionsтАЛ)тИТ(Sumeven┬аpositionsтАЛ)=0┬аor┬аmultiple┬аof┬а11
Calculate the alternating sum of digits (from right to left). If the result is 0 or divisible by 11, the number is divisible by 11.
Students often miscount the positions of the digits, leading to errors in the subtraction of the sums of even and odd positions.
Check 1234
Sum of odd positions (4+2=6) and even positions (3+1=4). The difference is 6-4=2, which is not 0 or a multiple of 11.
6тИТ4=2
Check 1331
Sum of odd positions (1+3=4) and even positions (3+1=4). The difference is 4-4=0, which confirms divisibility by 11.
4тИТ4=0
Check 1442
Sum of odd positions (2+4=6) and even positions (4+1=5). The difference is 6-5=1, which is not divisible by 11.
6тИТ5=1
Check 1553
Sum of odd positions (3+5=8) and even positions (5+1=6). The difference is 8-6=2, which is not divisible by 11.
8тИТ6=2
B is correct because 1331 is the only number whose alternating digit sum difference equals 0, confirming it is divisible by 11.
The divisibility rule for 11 is essential for simplifying fractions and identifying factors quickly in quantitative aptitude and mental ability sections.
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