The 7-digit number 12A916B is divisible by 24. What is the maximum value of (A + B)?
17
Divisible by 8 requires the last three digits '16B' to be divisible by 8: \(160+B\) must be divisible by 8, giving B=0 or B=8 (since 160 is already divisible by 8).
Divisible by 3 requires the digit sum \(1+2+A+9+1+6+B = 19+A+B\) to be divisible by 3.
Testing B=8 (larger value): \(27+A\) must be divisible by 3, so A must be a multiple of 3; the maximum digit is A=9.
Check: number 1291968 has last three digits 968 (divisible by 8) and digit sum 36 (divisible by 3) — both conditions hold.
Maximum \(A+B = 9+8 = 17\).
Hence, the maximum value of (A+B) is 17.
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Important Questions from Divisibility and Remainder
If the 8-digit number 888x53y4 is divisible by 72, then what is the value of (7x + 2y), for the maximum value of y?
If all positive divisors of 132 are arranged in descending order, then what digit will be at unit place of first divisor ?
If 3 2019 is divided by 10, then what is the remainder?
The number 3798125P369 is divisible by 7. What is the value of the digit P?
Consider all 3-digit numbers (without repetition of digits) obtained using three non-zero digits which are multiples of 3. Let S be their sum.
Which of the following is/are correct?
1. S is always divisible by 74.
2. S is always divisible by 9.
select the correct answer using the code given below:
