Question 23
A binary operation $\diamondsuit$ has the properties that $$
a\,\diamondsuit\, (b\,\diamondsuit \,c) = (a\,\diamondsuit \,b)\cdot c
$$ and that $a\,\diamondsuit \,a=1$ for all nonzero real numbers $a,$ $b,$ and $c.$ (Here the dot $\cdot$ represents the usual multiplication operation.) The solution to the equation $$
2016 \,\diamondsuit\, (6\,\diamondsuit\, x)=100
$$ can be written as $\frac{p}{q},$ where $p$ and $q$ are relatively prime positive integers. What is $p+q?$
a\,\diamondsuit\, (b\,\diamondsuit \,c) = (a\,\diamondsuit \,b)\cdot c
$$ and that $a\,\diamondsuit \,a=1$ for all nonzero real numbers $a,$ $b,$ and $c.$ (Here the dot $\cdot$ represents the usual multiplication operation.) The solution to the equation $$
2016 \,\diamondsuit\, (6\,\diamondsuit\, x)=100
$$ can be written as $\frac{p}{q},$ where $p$ and $q$ are relatively prime positive integers. What is $p+q?$