Find the value of k in the number 9314k8025 so that the number is divisible by 11.
- A2
- B6
- C4
- D5
Solution & Step-by-step Explanation
A number is divisible by 11 if the absolute difference between the sum of the digits at odd positions and the sum of the digits at even positions is either 0 or a multiple of 11.
Let's look at the positions from right to left for the number 9314k8025:
Sum of digits at odd positions (5th, 3rd, 1st...):
Sum
odd
=5+0+k+1+9=15+k
Sum of digits at even positions (4th, 2nd...):
Sum
even
=2+8+4+3=17
The difference must be a multiple of 11 or 0:
Difference=(15+k)−17=k−2
For k−2=0, we get:
k=2
Since 2 is a single-digit integer (0≤k≤9), k=2 is correct.
Let's look at the positions from right to left for the number 9314k8025:
Sum of digits at odd positions (5th, 3rd, 1st...):
Sum
odd
=5+0+k+1+9=15+k
Sum of digits at even positions (4th, 2nd...):
Sum
even
=2+8+4+3=17
The difference must be a multiple of 11 or 0:
Difference=(15+k)−17=k−2
For k−2=0, we get:
k=2
Since 2 is a single-digit integer (0≤k≤9), k=2 is correct.