Art of Problem Solving

2003 AMC 12B Problems/Problem 1: Difference between revisions

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==Solution==
==Solution==
<math>2-4+6-8+10-12+14=-2-2-2+14=8</math>
<cmath>
 
\begin{align*}
 
2-4+6-8+10-12+14=-2-2-2+14&=8\\
 
3-6+9-12+15-18+21=-3-3-3+21&=12\\
<math>3-6+9-12+15-18+21=-3-3-3+21=12</math>
\frac{2-4+6-8+10-12+14}{3-6+9-12+15-18+21}&=\frac{8}{12}=\frac{2}{3} \Rightarrow \text {(C)}
 
\end{align*}</cmath>
 
 
<math>\frac{2-4+6-8+10-12+14}{3-6+9-12+15-18+21}=\frac{8}{12}=\frac{2}{3} \Rightarrow \text {(C)}</math>


==See also==
==See also==
{{AMC12 box|year=2003|ab=B|before=First Question|num-a=2}}
{{AMC12 box|year=2003|ab=B|before=First Question|num-a=2}}
[[Category:Introductory Algebra Problems]]

Revision as of 17:08, 5 February 2008

Problem

Which of the following is the same as

\[\frac{2-4+6-8+10-12+14}{3-6+9-12+15-18+21}\]?

$\text {(A) } -1 \qquad \text {(B) } -\frac{2}{3} \qquad \text {(C) } \frac{2}{3} \qquad \text {(D) } 1 \qquad \text {(E) } \frac{14}{3}$

Solution

\begin{align*} 2-4+6-8+10-12+14=-2-2-2+14&=8\\ 3-6+9-12+15-18+21=-3-3-3+21&=12\\ \frac{2-4+6-8+10-12+14}{3-6+9-12+15-18+21}&=\frac{8}{12}=\frac{2}{3} \Rightarrow \text {(C)} \end{align*}

See also

2003 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
First Question
Followed by
Problem 2
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All AMC 12 Problems and Solutions