2016 AMC 10A Problems/Problem 23
A binary operation has the properties that and that for all nonzero real numbers and . (Here represents multiplication). 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)
See Also
2016 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem Problem 22 |
Followed by Problem 24 | |
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