Which of the following numbers is divisible by 11?

Correct option is D

Concept Used:

A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is a multiple of 11 (including 0).

Solution:

(A) 715896

Odd positions (1st, 3rd, 5th digits): 7, 5, 9

Sum = 7 + 5 + 9 = 21

Even positions (2nd, 4th, 6th digits): 1, 8, 6

Sum = 1 + 8 + 6 = 15

Difference = 21 - 15 = 6

Since 6 is not divisible by 11, 715896 is not divisible by 11.

(B) 715876

Odd positions: 7, 5, 7

Sum = 7 + 5 + 7 = 19

Even positions: 1, 8, 6

Sum = 1 + 8 + 6 = 15

Difference = 19 - 15 = 4

Since 4 is not divisible by 11, 715876 is not divisible by 11.

(C) 715859

Odd positions: 7, 5, 5

Sum = 7 + 5 + 5 = 17

Even positions: 1, 8, 9

Sum = 1 + 8 + 9 = 18

Difference = 17 - 18 = -1

Since -1 is not divisible by 11, 715859 is not divisible by 11.

(D) 715891

Odd positions: 7, 5, 9

Sum = 7 + 5 + 9 = 21

Even positions: 1,8,11, 8, 1

Sum = 1 + 8 + 1 = 10

Difference = 21 - 10 = 11

Since 11 is divisible by 11, 715891 is divisible by 11