Discussion
The number 1y3y8 is divisible by 11. What is the value of the digit y?
Answer: A
For a number to be divisible by 11, the difference between the sum of digits at odd places and the sum of digits at even places must be either 0 or a multiple of 11.
The number is 1y3y8.
Sum of digits at odd places (from the right): \(8 + 3 + 1 = 12\).
Sum of digits at even places (from the right): \(y + y = 2y\).
The difference is \(|12 - 2y|\).
We need \(|12 - 2y|\) to be 0 or a multiple of 11. Let's set the difference to 0.
\(12 - 2y = 0 \implies 2y = 12 \implies y = 6\).
Since y=6 is a valid single digit, this is our answer.
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