Which of the following numbers is divisible by 11? 

Calculation:

Divisibility rule of 11

This rule states that the given number can only be completely divided by 11 if the sum of digits at an odd position and the sum of digits at an even position in a number is 0 or 11.

(1)  97174

A sum of digits at even positions = 9 + 1 + 4 = 14

A sum of digits at odd positions = 7 + 7 = 14

Difference = 14 - 14 = 0

Since the difference is 0, 97174 is divisible by 11.

(2) 56923 

A sum of digits at even positions = 5 + 9 + 3 = 17

A sum of digits at odd positions = 6 + 2  = 8

Difference = 17 - 8 = 9

Since the difference is not a multiple of 11, 56923 is not divisible by 11.

(3) 63962 

A sum of digits at even positions = 3 + 6 = 9

A sum of digits at odd positions = 6 + 9 + 2 = 17

Difference = 17 - 9 = 8

Since the difference is not a multiple of 11, 63962 is not divisible by 11.

(4) 17295

A sum of digits at even positions = 1 + 2 + 5 = 8

A sum of digits at odd positions = 7 + 9 = 16

Difference = 16 - 8 = 8

Since the difference is not a multiple of 11, 17295 is not divisible by 11.

∴The number that is divisible by 11 is 97174.