Question

If A833B is divisible by 88, then find A and B.

• A. A = 6 and B = 2
• B. A = 2 and B = 6
• C. A = 1 and B = 2
• D. A = 3 and B = 0

Answer 1

The correct option is B A = 2 and B = 6

Since, A833B is divisible by 88, it will also be divisible by its factors 8 and 11 as 88 = 11 x 8

Divisibility of 11: If the difference between the sum of digits in odd places and sum of digits in even places of a number is a multiple of 11 or equal to zero, then the given number is divisibleby 11.

Digits at odd places = A + 3 + B
Digits at even places = 8 + 3
Difference
(A + 3 + B) - (8 + 3) = 0
A + B - 8 = 0
A + B = -8.... (i)

Divisibility of 8: If in a given number, the number formed by its last 3 digits is divisible by 8 or last 3 digits are ‘0’s, then given number is divisible by 8.

33B is diviisble by 8.
So, on dividing 33B by 8, the only possible value of B will be 6.
B = 6
Now, putting B in equation (i)
A + B = 8
A + 6 = 8
A = 8 - 6
A = 2
$\therefore$ The value of A = 2 and B = 6.