Difference between revisions of "2020 AMC 10B Problems/Problem 7"
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+ | == Video Solution == | ||
+ | https://youtu.be/ZhAZ1oPe5Ds?t=2241 | ||
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+ | ~ pi_is_3.14 | ||
==See Also== | ==See Also== | ||
{{AMC10 box|year=2020|ab=B|num-b=6|num-a=8}} | {{AMC10 box|year=2020|ab=B|num-b=6|num-a=8}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 21:20, 17 January 2021
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.