What is the smallest number that must be added to 19487161 so that it is divisible by 11?

The correct option is 10.

To determine the smallest number that must be added to 19487161 to make it divisible by 11, we use the divisibility rule for 11.

A number is divisible by 11 if the difference between the sum of the digits in odd positions (from right to left) and the sum of the digits in even positions is either 0 or a multiple of 11.

Let's calculate the sum of digits at odd and even positions for the number 19487161:

Sum of digits at odd positions (1^st, 3^rd, 5^th, 7^th from the right):
1 + 1 + 8 + 9 = 19

Sum of digits at even positions (2^nd, 4^th, 6^th, 8^th from the right):
6 + 7 + 4 + 1 = 18

Now, compute the difference:
Difference = 19 - 18 = 1

Since the remainder when 19487161 is divided by 11 is 1, the smallest number that must be added to make it a multiple of 11 is:

$11-1=10$

Therefore, 10 must be added to 19487161 to make it divisible by 11.