If 1234567y is divisible by 11, then what is the value of y?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 4.
Divisibility rule of 11:- A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is either 0 or a multiple of 11.
The number is 1234567y
The sum of Odd positions = 1 + 3 + 5 + 7 = 16
The sum of Even positions = 2 + 4 + 6 + y = 12 + y
The difference between the sum of the digits in odd positions and the sum of the digits in even positions should be 0 or a multiple of 11
Difference/11= ((16 - (12 + y))/11 = (16 - 12 - y)/11
⇒ (16 - 12 - y)/11 = (4 - y)/11
if we put y = 4;
⇒ (4 - 4)/11 = 0/11 = 0
Thus, the value of y is 4