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

Revision as of 14:50, 12 July 2017

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

$\begin{eqnarray*} U-V&=&2004*2004^{2004}\\ V-W&=&1*2004^{2004}\\ W-X&=&2001*2004^{2004}\\ X-Y&=&1*2004^{2004}\\ Y-Z&=&2003*2004^{2003} \end{eqnarray*}$

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

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

Revision as of 14:50, 12 July 2017

Problem

Solution

See Also

@@ Line 7: / Line 7: @@
 <cmath>\begin{eqnarray*}
 U-V&=&2004*2004^{2004}\\
-V-W&=&2004^{2004}\\
+V-W&=&1*2004^{2004}\\
 W-X&=&2001*2004^{2004}\\
-X-Y&=&2004^{2004}\\
+X-Y&=&1*2004^{2004}\\
 Y-Z&=&2003*2004^{2003}
 \end{eqnarray*}</cmath>