A: 6
To determine if a number divisible by 11, add up the odd digits and compare that to the sum of the even digits. For example, 242 is divisible by 11 because the 1st digit (2) and 3rd digit (2) add up to 4 and is equivalent to the (only) even digit.
Zip Code 10471: the odd digits (digits 1, 3, 5) are 1, 4, 1 and add up to 6 while the even digits (digits 2 and 4) add up to 7. Therefore 10471 is not divisible by 11.
Zip Code 10065: the wealthiest zip code in the United States IS divisible by 11 as the odd digits (digits 1, 3, 5) are 1, 0, 5 and add up to 6 while the even digits (digits 2 and 4) add up to 6. Therefore 10065 is divisible by 11.
Therefore:
In the number 6X92114. the odd digits are: 6 9 1 4 and add up to 20
The even digits are x 2 1 and add up to x + 3
If we set x + 3 = 20 then x would be 17 which cannot fit in one digit
So we have to think about what happens when the numbers add up to more than 11
For example 990 is divisible by 11 as is 979 and 968 -- notice that in 979 the sum of the odd digits is 11 more than the even digit (9 + 9 is 11 more than 7). This is also true in 968 as the sum of the odd digits is 17 which is 11 more than the even digit of 6.
For 6X92114, if we set x + 3 = 20 then x would be 17 which cannot fit in one digit but just like 968, we can use a 6 instead of a 17 (notice that 6 is 11 away from 17!)
