2020 AIME I Problems: Difference between revisions
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==Problem 2== | ==Problem 2== | ||
There is a unique positive real number <math>x</math> such that the three numbers <math>\log_8(2x),\log_4x,</math> and <math>\log_2x,</math> in that order, form a geometric progression with positive common ratio. The number <math>x</math> can be written as <math>\tfrac{m}{n},</math> where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m+n.</math> | |||
Revision as of 15:29, 12 March 2020
| 2020 AIME I (Answer Key) | AoPS Contest Collections • PDF | ||
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Instructions
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| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
to 
, inclusive. Your score will be the number of correct answers; i.e., there is neither partial credit nor a penalty for wrong answers.Problem 1
Problem 2
There is a unique positive real number 
such that the three numbers 
and 
in that order, form a geometric progression with positive common ratio. The number can be written as 
where 
and 
are relatively prime positive integers. Find 
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
| 2020 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by 2019 AIME II |
Followed by 2020 AIME II | |
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| All AIME Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: Unable to save thumbnail to destination
