Difference between revisions of "2005 AMC 10A Problems/Problem 2"

(Problem)
m (Problem)
Line 1: Line 1:
 
==Problem==
 
==Problem==
For each pair of real numbers <math>a\neqb</math>, define the [[operation]] <math>\star</math> as
+
For each pair of real numbers <math>a \neq b</math>, define the [[operation]] <math>\star</math> as
  
 
<math> (a \star b) = \frac{a+b}{a-b} </math>.
 
<math> (a \star b) = \frac{a+b}{a-b} </math>.

Revision as of 16:11, 27 June 2014

Problem

For each pair of real numbers $a \neq b$, define the operation $\star$ as

$(a \star b) = \frac{a+b}{a-b}$.

What is the value of $((1 \star 2) \star 3)$?

$\mathrm{(A) \ } -\frac{2}{3}\qquad \mathrm{(B) \ } -\frac{1}{5}\qquad \mathrm{(C) \ } 0\qquad \mathrm{(D) \ } \frac{1}{2}\qquad \mathrm{(E) \ } \textrm{This\, value\, is\, not\, defined.}$

Solution

$((1 \star 2) \star 3) = \left(\left(\frac{1+2}{1-2}\right) \star 3\right) = (-3 \star 3) = \frac{-3+3}{-3-3} = 0 \Longrightarrow \mathrm{(C)}$

See Also

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png