Find the sum of all the possible values of k in the number 341k145k so that the number is divisible by 3.
- A15
- B18
- C12
- D9
Solution & Step-by-step Explanation
A number is divisible by 3 if the sum of its digits is divisible by 3.
Sum of digits of 341k145k:
Sum=3+4+1+k+1+4+5+k=18+2k
For the number to be divisible by 3, (18+2k) must be a multiple of 3.
Since 18 is already a multiple of 3, 2k must also be a multiple of 3. This means k must be a multiple of 3.
Since k is a single-digit integer (0≤k≤9), the possible values for k are:
k=0,3,6,9
Sum of all possible values of k:
Sum=0+3+6+9=18
Sum of digits of 341k145k:
Sum=3+4+1+k+1+4+5+k=18+2k
For the number to be divisible by 3, (18+2k) must be a multiple of 3.
Since 18 is already a multiple of 3, 2k must also be a multiple of 3. This means k must be a multiple of 3.
Since k is a single-digit integer (0≤k≤9), the possible values for k are:
k=0,3,6,9
Sum of all possible values of k:
Sum=0+3+6+9=18