If 7-digit number 485A64B is divisible by 8 and 9, then find the greatest value of A + B.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 9
A number is divisible by 8 if its last three digits form a number divisible by 8, and by 9 if the sum of its digits is divisible by 9.
Divisible by 8 (last three digits 64B):
Of 640 to 649, only 640 and 648 are divisible by 8, so B = 0 or 8
Divisible by 9 (digit sum):
\(4+8+5+A+6+4+B=27+A+B\), so A + B must be 0, 9 or 18
A + B = 18 needs A = B = 9, which is ruled out because B is 0 or 8
A + B = 9 works with B = 0, A = 9 (4859640) or B = 8, A = 1 (4851648)
So the greatest value of A + B is 9.