Difference between revisions of "2014 AIME I Problems"

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==Problem 2==  
 
==Problem 2==  
An urn contains <math>4</math> green balls and <math>6</math> blue balls. A second urn contains <math>16</math> green bals and <math>N</math> 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 <math>N</math>
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An urn contains <math>4</math> green balls and <math>6</math> blue balls. A second urn contains <math>16</math> green bals and <math>N</math> 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 <math>N</math>.
  
  

Revision as of 05:01, 14 March 2014

2014 AIME I (Answer Key)
Printable version | AoPS Contest Collections

Instructions

  1. This is a 15-question, 3-hour examination. All answers are integers ranging from $000$ to $999$, inclusive. Your score will be the number of correct answers; i.e., there is neither partial credit nor a penalty for wrong answers.
  2. No aids other than scratch paper, graph paper, ruler, compass, and protractor are permitted. In particular, 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 $4$ green balls and $6$ blue balls. A second urn contains $16$ green bals and $N$ 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 $N$.


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

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