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, rulers and compasses are permitted. In particular, graph paper, protractors, calculators and computers are not permitted.

1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15

Problem 1

Solution

Problem 2

An urn contains green balls and blue balls. A second urn contains green bals 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

Solution

Problem 4

Solution

Problem 5

Solution

Problem 6

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

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.