Difference between revisions of "2004 AMC 12A Problems/Problem 6"
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<cmath>\begin{eqnarray*} | <cmath>\begin{eqnarray*} | ||
U-V&=&2004*2004^{2004}\\ | U-V&=&2004*2004^{2004}\\ | ||
| − | V-W&=&2004^{2004}\\ | + | V-W&=&1*2004^{2004}\\ |
W-X&=&2001*2004^{2004}\\ | W-X&=&2001*2004^{2004}\\ | ||
| − | X-Y&=&2004^{2004}\\ | + | X-Y&=&1*2004^{2004}\\ |
Y-Z&=&2003*2004^{2003} | Y-Z&=&2003*2004^{2003} | ||
\end{eqnarray*}</cmath> | \end{eqnarray*}</cmath> | ||
After comparison, <math>U-V</math> is the largest. <math>\mathrm {(A)}</math> | After comparison, <math>U-V</math> is the largest. <math>\mathrm {(A)}</math> | ||
| + | |||
| + | |||
| + | ==Solution 2== | ||
| + | A quick check reveals the positive integers are in decreasing order. Then note <math>V = 2004^{2005}</math>. <math>\newline</math> | ||
| + | <math>U - V = 2004^{2005} = V</math>, and any of the other differences cannot be greater than or equal to <math>V</math>, hence choose <math>\boxed{A}</math> as the answer. | ||
==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}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 01:10, 30 December 2020
Contents
Problem
Let 
, 
, 
, 
, 
and 
. Which of the following is the largest?
Solution
After comparison, 
is the largest. 
Solution 2
A quick check reveals the positive integers are in decreasing order. Then note 
. 
, and any of the other differences cannot be greater than or equal to 
, hence choose 
as the answer.
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 | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
