If \(x\) and \(y\) are the two digits of the number \(653xy\) such that this number is divisible by 80, then what is the value of \(x+y\)?
Answer: D
A number is divisible by 80 if it is divisible by both 10 and 8.
For the number to be divisible by 10, its last digit must be 0. So, \(y=0\).
The number now is \(653x0\).
For the number to be divisible by 8, the number formed by its last three digits must be divisible by 8. So, \(3x0\) must be divisible by 8.
Let's check values for x:
If x=2, the number is 65320. \(65320 \div 80 = 816.5\) (Not divisible).
If x=6, the number is 65360. \(65360 \div 80 = 817\) (Divisible).
So the number is 65360, which means \(x=6\) and \(y=0\).
The value of \(x+y = 6+0 = 6\).