2004 AMC 12A Problems/Problem 6

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

$U-V=2004^{2005}$

$V-W=2004^{2004}$

$W-X=2001*2004^{2004}$

$X-Y=2004^{2004}$

$Y-Z=2003*2004^{2003}$

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

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2004 AMC 12A Problems/Problem 6

Problem

Solution

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