Question : If the number 6336633P is divisible by 132, then the value of P is:
Option 1: 4
Option 2: 2
Option 3: 3
Option 4: 6
Correct Answer: 6
Solution :
The number 132 is divisible by both 11 and 12. So, for a number to be divisible by 132, it must be divisible by both 11 and 12.
Divisibility rule of 11: A number is divisible by 11 if the difference between the sum of digits at odd places and the sum of digits at even places is either 0 or a number that is divisible by 11.
For the number 6336633P to be divisible by 11,
(6 – P) = 0 ⇒ P = 6
Divisibility rule of 12: If P = 6, the quotient is 5280528, and the remainder is 0. Therefore, the number is divisible by 12.
Hence, the correct answer is 6.
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