Category: Arithmetic
"Published in Newark, California, USA"
Find the missing digit so that it becomes divisible by 6 for
a. 45?673
b. 34562?
Solution:
a. Consider the given number
Since the last digit of a given number is an odd number, then it is not divisible by 6. A number is divisible by 6 if it is both divisible by 2 and 3. All even numbers are divisible by 2. There's
nothing that we can do in
order to become divisible by 6 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 6.
b. Consider the given number
A number is divisible by 6 if it is both divisible by 2 and 3. In short, an even number that is divisible by 3. Add all the digits of the given number as follows
Since 20 is not a multiple of 3, then we need to add a number so that it becomes a multiple of 3. So, 20 + 1 = 21.
We can add also 4 (1 + 3) so that 20 + 4 = 24. We can add also 7 (1 + 3
+ 3) so that 20 + 7 = 27. 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. The numbers 1, 4, and 7 are the right digits to fill up the missing digit in order to become the given number divisible by 3.
Since we want a given number to be divisible by 6, then we have to choose 4 as a digit because the missing digit is the last digit. The last digit must be an even number so that the given number becomes divisible by 6. Therefore, the possible number is 345624.
Category: Arithmetic
"Published in Newark, California, USA"
Find the missing digit so that it becomes divisible by 5 for
a. 94?763
b. 32178?
Solution:
a. Consider the given number
Since the last digit of the given number is 3, then it is not divisible by 5. A number is divisible by 5 if the last digit is 5 or 0. There's
nothing that we can do in
order to become divisible by 5 since the last digit of a given number is
not 5 or 0. You can assign any number to the missing digit but
still, the given number will never become divisible by 5.
b. Consider the given number
A number is divisible by 5 if the last digit is 5 or 0. Since the missing digit is the last digit, then we can assign 5 and 0 so that the given number becomes divisible by 5. Therefore, the possible numbers are 321785 and 321780.
Category: Arithmetic
"Published in Newark, California, USA"
Find the missing digit so that it becomes divisible by 4 for
a. 5?627
b. 6721?
Solution:
a. Consider the given number
Since
the last two digit of a given number which is 27 is not a multiple of 4, then the
given number is not divisible by 4. There's nothing that we can do in
order to become divisible by 4 since the last digit of a given number is not a multiple of 4. You can assign any number to the missing digit but
still, the given number will never become divisible by 4.
b. Consider the given number
A number is divisible by 4 if the last two digit is a multiple of 4. Since 1 is located at the second to the last digit, then we can assign 2 and 6 to the last digit so that 1 becomes 12 and 16 which are the multiples of 4. Therefore, the possible numbers are 67212 and 67216.
