2020 AMC 10B Problems/Problem 7
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
Video Solution
https://youtu.be/ZhAZ1oPe5Ds?t=2241
~ pi_is_3.14
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. 
