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Difference between revisions of "2004 AMC 10A Problems/Problem 2"

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Education, the Study of Everything
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== Problem ==
 
== Problem ==
 
For any three real numbers <math>a</math>, <math>b</math>, and <math>c</math>, with <math>b\neq c</math>, the operation <math>\otimes</math> is defined by:
 
For any three real numbers <math>a</math>, <math>b</math>, and <math>c</math>, with <math>b\neq c</math>, the operation <math>\otimes</math> is defined by:

Revision as of 11:40, 20 December 2020

Video Solution

https://youtu.be/KfjB4--G-Lc

Education, the Study of Everything



Problem

For any three real numbers $a$, $b$, and $c$, with $b\neq c$, the operation $\otimes$ is defined by: \[\otimes(a,b,c)=\frac{a}{b-c}\] What is $\otimes(\otimes(1,2,3),\otimes(2,3,1),\otimes(3,1,2))$?

$\mathrm{(A) \ } -\frac{1}{2}\qquad \mathrm{(B) \ } -\frac{1}{4} \qquad \mathrm{(C) \ } 0 \qquad \mathrm{(D) \ } \frac{1}{4} \qquad \mathrm{(E) \ } \frac{1}{2}$

Solution

$\otimes \left(\frac{1}{2-3},\frac{2}{3-1},\frac{3}{1-2}\right)=\otimes(-1,1,-3)=\frac{-1}{1+3}=-\frac{1}{4}\Longrightarrow\boxed{\mathrm{(B)}\ -\frac{1}{4}}$

See also

2004 AMC 10A (Problems • Answer Key • Resources)
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Problem 1 		Followed by
Problem 3
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All AMC 10 Problems and Solutions

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