2003 AMC 10B Problems/Problem 1

Problem

Which of the following is the same as $\dfrac{2-4+6-8+10-12+14}{3-6+9-12+15-18+21}$ ?

$\textbf{(A)}\ -1 \qquad \textbf{(B)}\ -\frac23 \qquad \textbf{(C)}\ \frac23 \qquad \textbf{(D)}\ 1 \qquad \textbf{(E)}\ \frac{14}{3}$

We can rewrite the given fraction as:

$\frac{-3(2)+2(7)}{3(-3)+3(7)}=\frac{2(4)}{3(4)}=\frac{2}{3} \longrightarrow \boxed{\textbf{(C)}}$

2003 AMC 10B (Problems • Answer Key • Resources)
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