Question

Question 72

If 148101B095 is divisible by 33, find the value of B.

Answer 1

Given that the number 148101B095 is divisible by 33, therefore it is also divisible by 3 and 11 both.
Now, the number is divisible by 3. Its sum of digits is a multiple of 3.
i.e. 1 + 4 + 8 + 1 + 0 + 1 + B + 0 + 9 + 5 is a multiple 3.
29 + B = 0, 3, 6, 9,......
$\Rightarrow$ B = 1, 4, 7 ..............(i)
Also, given number is divisible by 11, therefore
(1 + 8 + 0 + B + 9) - (4 + 1 + 1+ 0 + 5) = 0, 11, 22, .....
$\Rightarrow$ (18 + B) - 11 = 0, 11, 22....
B + 7 = 0, 11, 22
$\Rightarrow$ B + 7 = 11 $\Rightarrow$ B = 4 .............(ii)
From Eqs. (i) and (ii), we have B = 4