Q. If the number K35624 is divisible by 11, then what is the value of K?

The correct answer is (D) 6.

Explanation:

Divisibility Rule for 11:

A number is divisible by 11 if the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is either 0 or a multiple of 11.

Applying the Rule to K35624:

Let’s assign positions to each digit from left to right:

Position: 1 2 3 4 5 6
Digit: K 3 5 6 2 4

1. Sum of digits in odd positions (1, 3, 5):
Sum_odd = K + 5 + 2 = K + 7

2. Sum of digits in even positions (2, 4, 6):
Sum_even = 3 + 6 + 4 = 13

3. Calculate the difference:
Difference = Sum_odd – Sum_even = (K + 7) – 13 = K – 6

For the number to be divisible by 11:
K – 6 ≡ 0 (mod 11)
K – 6 = 0 or K – 6 = ±11

Since K is a single digit (0-9):
K – 6 = 0 implies K = 6
Other possibilities (K = 17 or K = -5) are not valid as K must be a single digit.

Answer: (D) 6