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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.