Discussion
If the number 7x81y6 is divisible by 36, and y can be 7, what is the value of \(x-y\)?
Answer: A
For a number to be divisible by 36, it must be divisible by both 4 and 9.
1. Divisibility by 4: The number formed by the last two digits, y6, must be divisible by 4. If we take the given possibility of y=7, we get 76, which is divisible by 4 (\(19 \times 4 = 76\)).
2. Divisibility by 9: The sum of the digits must be divisible by 9. The number is 7x8176. Sum = \(7+x+8+1+7+6 = 29+x\). For this sum to be a multiple of 9, the closest multiple is 36. So, \(29+x=36\), which gives \(x=7\).
We have \(x=7\) and \(y=7\). Therefore, \(x-y = 7-7 = 0\).
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