What is the value of k such that number 72k460k is divisible by 6?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 4.
Co-prime factors of 6 = 2 and 3
72k460k is divisible by 6 which means that it is also divisible by 2 and 3.
The last digit of 72k460k is must be divisible by 2
Possible values of k = 0, 2, 4, 6, 8
Now according to the divisibility rule of 3,
The sum of the digits of 72k460k must be divisible by 3.
7 + 2 + k + 4 + 6 + 0 + k = 18 + 1 + 2k
18 is already a multiple of 3 so one can ignore this.
1 + 2k must be divisible by 3.
At k = 4 it satisfies
1 + 2 × 4 = 9.
k = 4.