If 148101B095 is divisible by 33,
Question:

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

Solution:

Given that the number 148101S095 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 Eqs. (i) and (ii), we have B = 4

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