1) In some cases, pairs of two-digit numbers have the same product as the two numbers read in reverse (for example $13 \times 62=31 \times 26$ ). How many two-digit numbers $A B$ (where $A$ and $B$ are decimal digits) are there such that $12 \times A B=21 \times B A$ ?
(A) 1
(B) 2
C) 3
(D) 4 (E) 9
1) The answer is (D). Since $12 \times A B$ is even, the digit $A$ must be even, and it must be $B=2 A$. Therefore, in addition to the obvious case $A=2$ which gives $12 \times 21=21 \times 12$, there are only the cases $A=4$, $A=6, A=8$ which provide $12 \times 42=21 \times 24,12 \times 63=21 \times 36,12 \times 84=21 \times 48$.