If a number 774958A96B is to be divisible by 8 and 9, the respective values of A and B will be
- 7 and 8
- 8 and 0
- 5 and 8
- None of this
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For divisiblity check of 8 is we divide last 3 numbers with 8.
So, 96B/8
for perfectly divisible B must be either 0 or 8.
Now, divisiblity check of 9 is to add all the numbers and check if it is divisible by 9 or not.
7 + 7 + 4 + 9 + 5 + 8 + A + 9 + 6 + B = 55 + A + B
lets take B = 0
55 + A + 0 = 55 + A
for the number divisible by both 9 and 8, A must be 8
We got (A, B) as (8, 0)
For case 2:
take B = 8
55 + A + 8 = 63 + A
for the number divisible by both 9 and 8, A must be 0, 9
We got (A, B) as (0, 8), (9, 8)
We have total 3 solutions for the answer (8, 0), (0, 8), (9, 8)
only 1 satisfy i.e. A=8 and B=0
So, option 2.