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 Question from Peter, a student: For what single digit value of n is the number n53nn672 divisible by 11?

Hi Peter,

The divisibility test for 11 states that the difference between the sum of the odd numbered digits (1st, 3rd, 5th, ...) and the sum of the even numbered digits (2nd, 4th, 6th, ...) must be divisible by 11 in order for the number itself to be divisible by 11.

Your number has 8 digits, the first of which is your unknown "n", the second digit is 5, the 3rd digit is 3...and so on. I will use a different set of 8 digits to illustrate the process and let you work out your problem similarly.

Let's say my number is 4nn187n2

The sum of the odd numbered digits is therefore 4 + n + 8 + n = 2n + 12
The sum of the odd numbered digits is therefore n + 1 + 7 + 2 = n + 10

(2n +12) - (n + 10) = n + 2

To be divisible by 11, the expression (n + 2) must be a multiple of 11.

Hint: non-negative multiples of 11 are: 0*11, 1*11, 2*11, 3*11, etc. or 0, 11, 22, 33, ...

Which single digit in place of n will result in a multiple of 11? Clearly it is 9, as 9 + 2 = 11.

As a check: 49918792 / 11 = 4538072

Hope this helps,
Leeanne

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.