Difference between revisions of "2003 AMC 12B Problems/Problem 1"

(New page: ==Problem== Which of the following is the same as <cmath>\frac{2-4+6-8+10-12+14}{3-6+9-12+15-18+21}</cmath>? <math> \text {(A) } -1 \qquad \text {(B) } -\frac{2}{3} \qquad \text {(C) } \...)
 
(Solution)
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==Solution==
 
==Solution==
 
<math>2-4+6-8+10-12+14=-2-2-2+14=8</math>
 
<math>2-4+6-8+10-12+14=-2-2-2+14=8</math>
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 +
  
 
<math>3-6+9-12+15-18+21=-3-3-3+21=12</math>
 
<math>3-6+9-12+15-18+21=-3-3-3+21=12</math>
 +
 +
  
 
<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>
 
<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==

Revision as of 10:06, 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

$2-4+6-8+10-12+14=-2-2-2+14=8$


$3-6+9-12+15-18+21=-3-3-3+21=12$


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

See also

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