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Difference between revisions of "Mock AIME 6 2006-2007 Problems"

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==Problem 1==
 
==Problem 1==
  
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Let <math>T</math> be the sum of all positive integers of the form <math>2^r\cdot3^s</math>, where <math>r</math> and <math>s</math> are nonnegative integers that do not exceed <math>4</math>.  Find the remainder when <math>T</math> is divided by 1000.
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Let <math>T</math> be the sum of all positive integers of the form <math>2^r\cdot3^s</math>, where <math>r</math> and <math>s</math> are nonnegative integers that do not exceed <math>4</math>.  Find the remainder when <math>T</math> is divided by <math>1000</math>.
  
 
[[Mock AIME 6 2006-2007 Problems/Problem 1|Solution]]
 
[[Mock AIME 6 2006-2007 Problems/Problem 1|Solution]]

Revision as of 13:15, 30 November 2014

Problem 1

Let $T$ be the sum of all positive integers of the form $2^r\cdot3^s$, where $r$ and $s$ are nonnegative integers that do not exceed $4$. Find the remainder when $T$ is divided by $1000$.

Solution

Problem 2

Solution

Problem 3

Solution

Problem 4

Solution

Problem 5

Solution

Problem 6

Solution

Problem 7

Solution

Problem 8

Solution

Problem 9

Solution

Problem 10

Solution

Problem 11

Solution

Problem 12

Solution

Problem 13

Solution

Problem 14

Solution

Problem 15

Solution

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