Difference between revisions of "2014 AIME I Problems"
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==Problem 3== | ==Problem 3== | ||
− | + | Find the number of rational numbers <math>r,</math> <math>0<r<1,</math> such that when <math>r</math> is written as a fraction in lowest terms, the numerator and the denominator have a sum of 1000. | |
[[2014 AIME I Problems/Problem 3|Solution]] | [[2014 AIME I Problems/Problem 3|Solution]] |
Revision as of 10:45, 14 March 2014
2014 AIME I (Answer Key) | AoPS Contest Collections • PDF | ||
Instructions
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1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 |
Contents
Problem 1
Problem 2
An urn contains green balls and
blue balls. A second urn contains
green balls and
blue balls. A single ball is drawn at random from each urn. The probability that both balls are of the same color is 0.58. Find
.
Problem 3
Find the number of rational numbers
such that when
is written as a fraction in lowest terms, the numerator and the denominator have a sum of 1000.
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.