Which of the following numbers is divisible by 11 .

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74,396

45,403

60,390

98,498

answer is C.

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Detailed Solution

Concept- To solve this problem, assume that the number is divisible by 11 and that, when the sum of the digits at even and odd places is subtracted, the result is either 0 or 11. Therefore, we will evaluate all the possibilities using this definition.
According to the well-known Divisibility Law of 11, the number of digits is reduced by the sum of the digits at odd places. The outcome is either 0 or divisible by 11
We will immediately do alternate testing.
1) 74,396
Here digits at odd places are 7,3,6
and digits at even places are 4,9
By using the divisibility rule of 11
Sum of digits at odd places - Sum of digits at even places

or 11
Substituting the values-

Here the result comes out as 3 therefore 74,396 is not divisible by 11 .
2) 45,403
Here digits at odd places are 4,4,3
and digits at even places are 5,0
By using the divisibility rule of 11
Sum of digits at odd places - Sum of digits at even places

or 11
Substituting the values-

Here the result comes out as 6 therefore 45,403 is not divisible by 11 .
3) 60,390
Here digits at odd places are 6,3,0
and digits at even places are 0,9
By using the divisibility rule of 11
Sum of digits at odd places - Sum of digits at even places

or 11
Substituting the values-

Here the result comes out as 0 therefore 60,390 is divisible by 11 .
4) 98,498
Here digits at odd places are 9,4,8
and digits at even places are 8,9
By using the divisibility rule of 11
Sum of digits at odd places - Sum of digits at even places

or 11
Substituting the values-

So, the result comes out as 4 therefore 98,498 is not divisible by 11 .
Hence, the correct answer is option 3.
Syllabus: CBSE

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