What is the digit y if the number 6y512 is exactly divisible by both 8 and 9?
4
A number is divisible by 8 when its last three digits form a number divisible by 8. Here the last three digits are 512, and \(512 \div 8 = 64\), so the divisibility-by-8 condition is satisfied for every value of y.
A number is divisible by 9 when the sum of its digits is divisible by 9. The digit sum is \(6 + y + 5 + 1 + 2 = 14 + y\).
For \(14 + y\) to be a multiple of 9, the next multiple after 14 is 18, so \(14 + y = 18\), giving \(y = 4\).
Hence, the digit y is 4.
Which of the following numbers is divisible by 7 ?