Difference between revisions of "2000 AMC 10 Problems/Problem 1"

Latest revision as of 15:37, 31 July 2009

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-==Problem==
+#REDIRECT [[2000 AMC 12 Problems/Problem 1]]
-In the year 2001, the United States will host the International Mathematical Olympiad. Let <math>I</math>, <math>M</math>, and <math>O</math> be distinct positive integers such that the product <math>I\cdot M\cdot O=2001</math>. What is the largest possible value of the sum <math>I+M+O</math>?
-==Solution==
-<math>2001=1\cdot 3\cdot 667=3\cdot 23\cdot 29</math>
-<math>1+3+667=671</math>
-<math>3+23+29=55</math>
-<math>1+29+69=99</math>
-<math>1+23+87=111</math>
-Clearly, <math>671</math>, or <math>\boxed{E}</math> is the largest.