Question 8
Let $A$, $B$, $C$ and $D$ be four positive two-digit integers: $A=\square5$, $B=\square3$, $C=7\square$ and $D=2\square$, where the $\square$ symbol does not necessarily represent the same digit in each of the numbers.
Given that:
- The sum of $A$, $B$, $C$ and $D$ is 180.
- The unit digits of $A$, $B$, $C$ and $D$ are all distinct.
- The unit digit of $D$ is greater than the unit digit of $C$.
- $D<A<B<C$.
What is the largest possible value of $A\times B$?
Given that:
- The sum of $A$, $B$, $C$ and $D$ is 180.
- The unit digits of $A$, $B$, $C$ and $D$ are all distinct.
- The unit digit of $D$ is greater than the unit digit of $C$.
- $D<A<B<C$.
What is the largest possible value of $A\times B$?