Difference between revisions of "2015 AIME I Problems"
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The expressions <math>A</math> = <math> 1 \times 2 + 3 \times 4 + 5 \times 6 + \cdots + 37 \times 38 + 39 </math> and <math>B</math> = <math> 1 + 2 \times 3 + 4 \times 5 + \cdots + 36 \times 37 + 38 \times 39 </math> are obtained by writing multiplication and addition operators in an alternating pattern between successive integers. Find the positive difference between integers <math>A</math> and <math>B</math>. | The expressions <math>A</math> = <math> 1 \times 2 + 3 \times 4 + 5 \times 6 + \cdots + 37 \times 38 + 39 </math> and <math>B</math> = <math> 1 + 2 \times 3 + 4 \times 5 + \cdots + 36 \times 37 + 38 \times 39 </math> are obtained by writing multiplication and addition operators in an alternating pattern between successive integers. Find the positive difference between integers <math>A</math> and <math>B</math>. | ||
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| + | ==Problem 2== | ||
| + | The nine delegates to the Economic Cooperation Conference include <math>2</math> officials from Mexico, <math>3</math> officials from Canada, and <math>4</math> officials from the United States. During the opening session, three of the delegates fall asleep. Assuming that the three sleepers were determined randomly, the probability that exactly two of the sleepers are from the same country is <math>\frac{m}{n}</math>, where m and n are relatively prime positive integers. Find <math>m+n</math>. | ||
Revision as of 16:56, 20 March 2015
Problem 1
The expressions 
= 
and 
= 
are obtained by writing multiplication and addition operators in an alternating pattern between successive integers. Find the positive difference between integers and .
Problem 2
The nine delegates to the Economic Cooperation Conference include 
officials from Mexico, 
officials from Canada, and 
officials from the United States. During the opening session, three of the delegates fall asleep. Assuming that the three sleepers were determined randomly, the probability that exactly two of the sleepers are from the same country is 
, where m and n are relatively prime positive integers. Find 
.
