a) A mighty dragon has several rubies in his treasure. He is able to
divide the rubies into groups of \(3\),
\(5\) or \(11\). How many rubies does he have, if we
know that is fewer than \(200\)?
b) The same dragon also has some emeralds. He is \(6\) emeralds short to be able to divide
them into groups of \(13\), one emerald
short to be able to divide them into groups of \(5\), but if he wants to divide them into
groups of \(8\), he is left with one
emerald. How many emeralds does he have if we know it is fewer than
\(500\)?