If 7-digit number 485A64B is divisible by 8 and 9, then find the greatest value of A + B.

9

If number is divisible by 8, last three digits are either 0 or divisible by 8

Since they are non zero, therefore the last three digits will be 640 or 648 with quotient 80 and 81 respectively.

So, B is 0 or 8

If number is divisible by 9, the sum of all the digits is divisible by 9,

Sum, if B is 0 = 4+8+5+A+6+4+0 = 27+A (So A is 0 or 9)

A+B = 0 or 9

Sum, if B is 8 = 4+8+5+A+6+4+8 = 35+A (So A is 1)

A+B = 9

Therefore highest value of A+B = 9

The correct answer is Option (3) → 9