Saturday, May 31, 2014

Finding Missing Digit - Divisibility Rule, 8

Category: Arithmetic

"Published in Vacaville, California, USA"

Find the missing digit so that it becomes divisible by 9 for

a. 13?84
b. 2096?

Solution:

a. Consider the given number

A number is divisible by 9 if the sum of the digits is a multiple of 9. If you add the rest of the digits, the sum will be equal to

Since 16 is not a multiple of 9, then we need to add a number so that it becomes a multiple of 9. So, 16 + 2 = 18. 2 is the highest digit that we can use because 2 + 9 = 11 will be a two digit number and we need to use only one digit to fill up the missing digit. Therefore, the possible number is 13284 only.

b. Consider the given number

A number is divisible by 9 if the sum of the digits is a multiple of 9. If you add the rest of the digits, the sum will be equal to

Since 17 is not a multiple of 9, then we need to add a number so that it becomes a multiple of 9. So, 17 + 1 = 18. 1 is the highest digit that we can use because 1 + 9 = 10 will be a two digit number and we need to use only one digit to fill up the missing digit. Therefore, the possible number is 20961 only.