Difference between revisions of "2020 AMC 10B Problems/Problem 7"
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Revision as of 14:38, 13 December 2020
Contents
Problem
How many positive even multiples of less than
are perfect squares?
Solution
Any even multiple of is a multiple of
, so we need to find multiples of
that are perfect squares and less than
. Any solution that we want will be in the form
, where
is a positive integer. The smallest possible value is at
, and the largest is at
(where the expression equals
). Therefore, there are a total of
possible numbers.-PCChess
Video Solution
Check It Out! Short & Straight-Forward Solution: Education, The Study of Everything
https://www.youtube.com/watch?v=igjvQv-TCGE
~IceMatrix
~savannahsolver
See Also
2020 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.