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Sunday, May 25, 2014

Finding Missing Digit - Divisibility Rule, 2

Category: Arithmetic

"Published in Newark, California, USA"

Find the missing digit so that it becomes divisible by 3 for

a. 35?83 
b. 7895? 

Solution:

a. Consider the given number


A number is divisible by 3 if the sum of the digits is a multiple of 3. If you add the rest of the digits, the sum will be equal to



Since 19 is not a multiple of 3, then we need to add a number so that it becomes a multiple of 3. So, 19 + 2 = 21. We can add also 5 (2 + 3) so that 19 + 5 = 24. We can add also 8 (2 + 3 + 3) so that 19 + 8 = 27. 8 is the highest digit that we can use because 8 + 3 = 11 will be a two digit number and we need to use only one digit to fill up the missing digit. Therefore, the possible numbers are 35283, 35583, and 35883.  

b. Consider the given number


A number is divisible by 3 if the sum of the digits is a multiple of 3. If you add the rest of the digits, the sum will be equal to

  

Since 29 is not a multiple of 3, then we need to add a number so that it becomes a multiple of 3. So, 29 + 1 = 30. We can add also 4 (1 + 3) so that 29 + 4 = 33. We can add also 7 (1 + 3 + 3) so that 29 + 7 = 36. 7 is the highest digit that we can use because 7 + 3 = 10 will be a two digit number and we need to use only one digit to fill up the missing digit. Therefore, the possible numbers are 78951, 78954, and 78957.