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.
Category: Arithmetic
"Published in Newark, California, USA"
Find the missing digit so that it becomes divisible by 8 for
a. 78?45
b. 2468?
Solution:
a. Consider the given number
Since
the last digit of a given number is not an even number, then the
given number is not divisible by 8. The multiples of 8 are all even number. There's nothing that we can do in
order to become divisible by 8 since the last digit of a given number is
not an even number. You can assign any number to the missing digit but
still, the given number will never become divisible by 8.
b. Consider the given number
A number is divisible by 8 if the last three digit is a multiple of 8. Since the missing digit is the last digit, then we can assign even number digits so that the last three digit will be divisible by 8. If the last digit is 0, then 68 becomes 680 and 680 is divisible by 8. If the last digit is 2, then 68 becomes 682 and 682 is not divisible by 8. If the last digit is 4, then 68 becomes 684 and 684 is not divisible by 8. If the last digit is 6, then 68 becomes 686 and 686 is not divisible by 8. If the last digit is 8, then 68 becomes 688 and 688 is divisible by 8. Therefore, the possible numbers are 24680 and 24688.
