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2004 AMC 12A Problems/Problem 6: Difference between revisions

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==Solution==
==Solution==
<math>\begin{eqnarray}
<cmath>\begin{eqnarray*}
U-V&=&2004^{2005}\\
U-V&=&2004^{2005}\\
V-W&=&2004^{2004}\\
V-W&=&2004^{2004}\\
Line 11: Line 11:
X-Y&=&2004^{2004}\\
X-Y&=&2004^{2004}\\
Y-Z&=&2003*2004^{2003}
Y-Z&=&2003*2004^{2003}
\end{eqnarray}</math>
\end{eqnarray*}</cmath>


After comparison, <math>(1)</math> is the largest. <math>\mathrm {(A)}</math>
After comparison, <math>U-V</math> is the largest. <math>\mathrm {(A)}</math>


==See Also==
==See Also==
{{AMC12 box|year=2004|ab=A|num-b=5|num-a=7}}
{{AMC12 box|year=2004|ab=A|num-b=5|num-a=7}}

Revision as of 12:49, 5 December 2007

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 (Problems • Answer Key • Resources)
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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