Discussion
The number 1y3y6 is divisible by 11. What is the value of the digit y?
Answer: C
Correct answer: 5
A number is divisible by 11 when the alternating sum of its digits is 0 or a multiple of 11. For 1y3y6, grouping the digits by position from the right:
\[(6 + 3 + 1) - (y + y) = 10 - 2y\]
This difference is always even, so it can never equal \(\pm 11\). The only remaining possibility is \(10 - 2y = 0\), which gives \(y = 5\).
The number is 15356, and \(15356 \div 11 = 1396\).
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