2016 AMC 10A Problems/Problem 23
A binary operation has the properties that
and that
for all nonzero numbers
and
. (Here the dot
represents the usual multiplication operation.) The solution to the equation
can be written as
, where
and
are relatively prime positive integers. What is
?
Solution
We see that , and think of division. Testing, we see that the first condition
is satisfied, because
. Therefore, division is the operation
. Solving the equation,
, so
, so the answer is
(A)