Question 19
Two distinct 2-digit prime numbers $p$, $q$ can be written one after the other in 2 different ways to form two 4-digit numbers. For example, $11$ and $13$ yield $1113$ and $1311$. If the two 4-digit numbers formed are both divisible by the average value of $p$ and $q$, find all possible pairs \{$p, q$\}.