2014 AIME I Problems

2014 AIME I (Answer Key) | AoPS Contest Collections • PDF

Instructions This is a 15-question, 3-hour examination. All answers are integers ranging from to , inclusive. Your score will be the number of correct answers; i.e., there is neither partial credit nor a penalty for wrong answers. No aids other than scratch paper, graph paper, ruler, compass, and protractor are permitted. In particular, calculators and computers are not permitted.

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Problem 1

Solution

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 .

Solution

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.

Solution

Problem 4

Solution

Problem 5

Solution

Problem 6

The graphs and have y-intercepts of 2013 and 2014, respectively, and each graph has two positive integer x-intercepts. Find .

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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.