Difference between revisions of "2018 AIME I Problems"

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==Problem 15==
 
==Problem 15==
  
 
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How many integers <math>n</math> leave a remainder of <math>\frac{n}{2}</math> when divided by a perfect square less than <math>100</math>?
  
 
[[2018 AIME I Problems/Problem 15 | Solution]]
 
[[2018 AIME I Problems/Problem 15 | Solution]]
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{{AIME box|year=2018|n=I|before=[[2017 AIME II]]|after=[[2018 AIME II]]}}
 
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How many integers <math>n</math> leave a remainder of <math>\frac{n}{2}</math> when divided by a perfect square less than <math>100</math>?
 

Revision as of 17:58, 6 March 2018

2018 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

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

How many integers $n$ leave a remainder of $\frac{n}{2}$ when divided by a perfect square less than $100$?

Solution

2018 AIME I (ProblemsAnswer KeyResources)
Preceded by
2017 AIME II
Followed by
2018 AIME II
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions

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

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