Category: Arithmetic
"Published in Newark, California, USA"
Find the missing digit so that it becomes divisible by 12 for
a. 234?89
b. 34524?
Solution:
a. Consider the given number
A number is divisible by 12 if it is both divisible by 3 and 4. Since the last digit of a given number is an odd number, then the given number is not divisible by 12. The multiples of 12 are all even number. There's nothing that we can do in
order to become divisible by 12 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 12.
b. Consider the given number
A number is divisible by 12 if it is both divisible by 3 and 4. Since the missing digit is the last digit, then we can assign even number digits so that the last two digit becomes divisible by 4. When you add all the digits, the sum should be a multiple of 3 so that the given number is divisible by 12. If the last digit is 0, then the last two digit becomes 40. The sum of the digits is 3 + 4 + 5 + 2 + 4 + 0 = 18. Since 18 is a multiple of 3, then 0 is the last digit. If the last digit is 4, then the last two digit becomes 44. The sum of the digits is 3 + 4 + 5 + 2 + 4 + 4 = 22. Since 22 is not a multiple of 3, then we cannot use 4 as the last digit. If the last digit is 8, then the last two digit becomes 48. The sum of the digits is 3 + 4 + 5 + 2 + 4 + 8 = 26. Since 26 is not a multiple of 3, then we cannot use also 8 as the last digit. Therefore, the possible number is 345240 only.
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.
