Discussion

If the number 732xy is divisible by 90, then what is the value of \(x+y\)?

Answer: D

For a number to be divisible by 90, it must be divisible by both 9 and 10.

1. Divisibility by 10: The last digit must be 0. So, \(y=0\).

2. Divisibility by 9: The sum of the digits must be divisible by 9. The number is now 732x0. The sum of digits is \(7+3+2+x+0 = 12+x\).

For \(12+x\) to be divisible by 9, the sum must be the next multiple of 9, which is 18. So, \(12+x = 18\), which gives \(x=6\).

We have \(x=6\) and \(y=0\). Therefore, \(x+y = 6+0 = 6\).

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