• # question_answer How many 5-digit numbers of the form AABAA is divisible by 33? A)  1                                B)  3                    C)  0                                D)  infinite

We have AABAA is divisible by 33. So, it is divisible by both 3 and 11. $\therefore \text{A + B + A - (A + A)=B}$ is divisible by 11. $\Rightarrow B=0$ Also, A+A+B+A+A=4A+B is divisible by 3. $\Rightarrow 4A$ is divisible by 3                   $(\because B=0)$ $\Rightarrow A$ is divisible by 3 Hence, possible values of A are 0, 3, 6, 9 But A can't be equal to zero. $\therefore$ Number of possible 5-digit numbers are 3.