2004 AMC 12A Problems/Problem 6: Difference between revisions
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==Solution 2== | ==Solution 2== | ||
A quick check reveals the positive integers are in decreasing order. Then note <math>V = | 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. | <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
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 | |
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