Difference between revisions of "2004 AMC 12A Problems/Problem 6"

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Revision as of 20:15, 3 July 2013

Problem

Let $U=2\cdot 2004^{2005}$, $V=2004^{2005}$, $W=2003\cdot 2004^{2004}$, $X=2\cdot 2004^{2004}$, $Y=2004^{2004}$ and $Z=2004^{2003}$. Which of the following is the largest?

$\mathrm {(A)} U-V \qquad \mathrm {(B)} V-W \qquad \mathrm {(C)} W-X \qquad \mathrm {(D)} X-Y \qquad \mathrm {(E)} Y-Z \qquad$

Solution

\begin{eqnarray*} U-V&=&2004^{2005}\\ V-W&=&2004^{2004}\\ W-X&=&2001*2004^{2004}\\ X-Y&=&2004^{2004}\\ Y-Z&=&2003*2004^{2003} \end{eqnarray*}

After comparison, $U-V$ is the largest. $\mathrm {(A)}$

See Also

2004 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
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 12 Problems and Solutions

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