Difference between revisions of "2024 AMC 10B Problems/Problem 25"
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~ Pi Academy | ~ Pi Academy | ||
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+ | ==Video Solution 2 by SpreadTheMathLove== | ||
+ | https://www.youtube.com/watch?v=24EZaeAThuE | ||
==See also== | ==See also== | ||
{{AMC10 box|year=2024|ab=B|num-b=24|after=Last Problem}} | {{AMC10 box|year=2024|ab=B|num-b=24|after=Last Problem}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 14:01, 14 November 2024
Contents
[hide]Problem
Each of bricks (right rectangular prisms) has dimensions , where , , and are pairwise relatively prime positive integers. These bricks are arranged to form a block, as shown on the left below. A th brick with the same dimensions is introduced, and these bricks are reconfigured into a block, shown on the right. The new block is unit taller, unit wider, and unit deeper than the old one. What is ?
Solution 1
The xx block has side lengths of . The xx block has side lengths of .
We can create the following system of equations, knowing that the new block has unit taller, deeper, and wider than the original:
Adding all the equations together, we get . Adding to both sides, we get . The question states that are all relatively prime positive integers. Therefore, our answer must be congruent to . The only answer choice satisfying this is . ~lprado
Video Solution 1 by Pi Academy (In Less Than 3 Mins ⚡🚀)
https://youtu.be/Xn1JLzT7mW4?feature=shared
~ Pi Academy
Video Solution 2 by SpreadTheMathLove
https://www.youtube.com/watch?v=24EZaeAThuE
See also
2024 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
Followed by Last Problem | |
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.