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

m (Problem)
(See Also)
Line 12: Line 12:
  
 
==See Also==
 
==See Also==
*[[2005 AMC 10A Problems]]
 
  
*[[2005 AMC 10A Problems/Problem 1|Previous Problem]]
+
{{AMC10 box|year=2005|ab=A|before=Problem 1|num-a=2}}
  
*[[2005 AMC 10A Problems/Problem 3|Next Problem]]
+
[[Category:Introductory Algebra Problems]]
 
 
[[Category:Introductory Algebra Problems]]
 
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 14:20, 13 August 2019

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

2005 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 2
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. AMC logo.png