## Monday, June 2, 2014

### Finding Missing Digit - Divisibility Rule, 10

Category: Arithmetic

"Published in Vacaville, California, USA"

Find the missing digit so that it becomes divisible by 11 for

a. 23?329
b. 39085?

Solution:

a. Consider the given number

To test the divisibility of a number by 11, group the sum of the alternating digits into two groups and then get their difference. If the result is a multiple of 11, then the given number is divisible by 11. Let's do this for the given number as follows

Since -11 is a multiple of 11, then we don't have to add any number so that it becomes a multiple of 11 and hence, 0 is the missing digit. Therefore, the possible number is 230329.

b. Consider the given number

To test the divisibility of a number by 11, group the sum of the alternating digits into two groups and then get their difference. If the result is a multiple of 11, then the given number is divisible by 11. Let's do this for the given number as follows

Since -9 is not a multiple of 11, then we need to add a number so that it becomes a multiple of 11. If you add -2 (add 2 at the second group), then the answer is -11. 2 is the highest digit that we can use. Therefore, the possible number is 390852