MathDB

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

\cdot

represents multiplication). The solution to the equation

2016 \,\diamondsuit\, (6\,\diamondsuit\, x)=100

can be written as

\tfrac{p}{q}

, where

p

and

q

are relatively prime positive integers. What is

p+q?

<span class='latex-bold'>(A) </span>109\qquad<span class='latex-bold'>(B) </span>201\qquad<span class='latex-bold'>(C) </span>301\qquad<span class='latex-bold'>(D) </span>3049\qquad<span class='latex-bold'>(E) </span>33,601

Problem Statement