Question

# Which of the following numbers are divisible by 11?

A

72512

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B

432

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C

7825

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D

1441

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Solution

## The correct options are A 72512 D 1441 A number is divisible by 11, if the difference of the sum of digits in odd places from the right and sum of its digits in even places from the right is divisible by 11. (a) 72512 The sum of its digits at even places = 2 + 1 = 3 The sum of its digits at odd places = 7 + 5 + 2 = 14 The difference between the two sums = 14 - 3 = 11 which is a multiple of 11. Hence, 72512 is divisible by 11. (b) 432 The sum of the digits in the odd places = 4 + 2 = 6 The digit in the even place = 3 The difference = 6 - 3 = 3 which is not divisible by 11. Hence, 432 is not divisible by 11. (c) 7825 The sum of the digits in the odd places = 7 + 2 = 9 The sum of the digits in the even place = 8 + 5 = 13 The difference = 13 - 9 = 4 which is not divisible by 11. Hence, 7825 is not divisible by 11. (d) 1441 The sum of the digit in the odd places = 4 + 1 = 5 The sum of the digits in the even places = 1 + 4 = 5 The difference = 5 - 5 = 0 which is divisible by 11. Hence, 1441 is divisible by 11.

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