If a seven-digit number 42971K2 is divisible by 44, then the value of K is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 7.
Seven-digit number = 42971K2
The number is divisible by 44, So, the number is also divisible by 11 and 4
4 Divisibility rule: The last two digits of the number should be divisible by 4.
So, possible value of K = 1, 3, 5, 7, 9
11 Divisibility rule: The difference between the sum of digits at odd places and the sum of digits at even places is 0 or 11.
For K = 1
⇒ (4 + 9 + 1 + 2) - (2 + 7 + 1)
⇒ 6 (Not divisible by 11)
For K = 3
⇒ (4 + 9 + 1 + 2) - (2 + 7 + 3)
⇒ 4 (Not divisible by 11)
For K = 5
(4 + 9 + 1 + 2) - (2 + 7 + 5)
⇒ 2 (Not divisible by 11)
For K = 7
⇒ (4 + 9 + 1 + 2) - (2 + 7 + 7)
⇒ 0 (divisible by 11)
For K = 9
⇒ (4 + 9 + 1 + 2) - (2 + 7 + 9)
⇒ -2 (Not divisible by 11)
So, the value of K = 7