If 3c2933k is divisible by both 5 and 11, where c and k are single digit natural numbers, then c + k = ______.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 6.
A number is divisible by 5 if its last digit is either 0 or 5
k must be either 0 or 5
A number is divisible by 11 if the difference between the sum of the digits at odd places and the sum of the digits at even places is either 0 or a multiple of 11.
Odd place: 3 + 2 + 3 + k = 8 + k
Even place: c + 9 + 3 = c + 12
Difference = (8 + k) - (c + 12) = k - c - 4
If k = 5, the difference is 5 - c - 4 = 1 - c
So, 1 - c is a multiple of 11
If 1 - c = 0, then c = 1
c + k = 1 + 5 = 6
Therefore, the value of c + k is 6.