1. How many 6-digit numbers are divisible by 33 and are palindromes, meaning they remain the same when read from right to left?
(A) 30
(B) 33
(C) 300
(D) 333
(E) None of the above.
1. The answer is $\mathbf{( C )}$. Since the number is a palindrome, we can write it as $a b c c b a$, where $a, b, c$ are digits and $a \neq 0$. The divisibility rule for 11 is then automatically satisfied, being $a-b+c-c+b-a=0$.

For the divisibility rule for 3, it is required that $2(a+b+c)$ be a multiple of 3, which means that the number $a b c$ must be a multiple of 3; the answer is thus the number of integers $100 \leq n \leq 999$ that are multiples of 3, which are $\frac{999-102}{3}+1=300$.