Question 35
Let $A = abcd = a \cdot 10^3 + b \cdot 10^2 + c \cdot 10 + d$ be a four digit positive integer such that: $a \ge 7$ and $a \gt b \gt c \gt d \gt 0$. We consider the positive integer $B = \overline{dcba} = d \cdot 10^3 + c \cdot 10^2 + b \cdot 10 + a$. If all digits of $A + B$ are odd, determine all possible values of $A$.