Difference between revisions of "2016 AMC 10A Problems/Problem 23"
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Revision as of 18:14, 3 February 2016
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 [[2016 AMC 10A Problems/Problem {{{num-b}}}|Problem {{{num-b}}}]] |
Followed by Problem 24 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
