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2004 AMC 12A Problems/Problem 6

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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

$\begin{eqnarray*}U-V&=&2004^{2005}\\V-W&=&2004^{2004}\\W-X&=&2001*2004^{2004}\\X-Y&=&2004^{20...$

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

See Also

2004 AMC 12A (Problems • 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

Retrieved from "http://www.artofproblemsolving.com/Wiki/index.php/2004_AMC_12A_Problems/Problem_6"

Looking for a challenging algebra text? Preparing for MATHCOUNTS or the AMC exams?
Check out Art of Problem Solving's Introduction to Algebra by Richard Rusczyk.

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