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.
Category: Arithmetic
"Published in Vacaville, California, USA"
Find the missing digit so that it becomes divisible by 10 for
a. 45?897
b. 32681?
Solution:
a. Consider the given number
Since
the last digit of the given number is 7, then it is not divisible by 10.
A number is divisible by 10 if the last digit is 0. There's
nothing that we can do in
order to become divisible by 10 since the last digit of a given number is
not 0. You can assign any number to the missing digit but
still, the given number will never become divisible by 10.
b. Consider the given number
A
number is divisible by 10 if the last digit is 0. Since the missing
digit is the last digit, then we can assign 0 so that the given
number becomes divisible by 10. Therefore, the possible number is 326810 only.
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.
