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Question
If 148101B095 is divisible by 33, find the value of B.
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Solution
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 of 3.
29 + B = 0, 3, 6, 9,...
⇒ 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,...
⇒ (18 + B) – 11 = 0, 11, 22
B + 7 = 0, 11, 22
⇒ B + 7 = 11
⇒ B = 4 ...(ii)
From equations (i) and (ii), we have
B = 4
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