Question

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

Answer 1

$148101B095$ is divisible by $33$. Therefore it is also divisible by $11$ and $3$

If a Number is divisible by $3$ then the sum of its digits is also divisible by $3$

Therefore $1+4+8+1+0+1+B+0+9+5=0,3,6,....$

$29+B=30,33,36$, as for higher values $B$ will become two digit number

$\Rightarrow B=1,4,7$

If a number divisible by $11$ then difference of sums of alternate digits is also divisible by $11$

$(1+8+0+B+9)-(4+1+1+0+5)=0,11,22,33,....$

Therefore, $B+7=11$, as for higher values $B$ will become two digit number

$\Rightarrow B=4$, which also satisfies condition for $3$