Difference between revisions of "2024 AMC 8 Problems/Problem 1"
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<cmath>222{,}222-22{,}222-2{,}222-222-22-2\equiv2-2-2-2-2\equiv-8\equiv\boxed{\textbf{(B) } 2}\pmod{10}</cmath> | <cmath>222{,}222-22{,}222-2{,}222-222-22-2\equiv2-2-2-2-2\equiv-8\equiv\boxed{\textbf{(B) } 2}\pmod{10}</cmath> | ||
− | == Video Solution 1 (Detailed Explanation) | + | == Video Solution 1 (Detailed Explanation)== |
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https://youtu.be/jqsbMWhTYRg | https://youtu.be/jqsbMWhTYRg | ||
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==Video Solution by Central Valley Math Circle (Goes through full thought process)== | ==Video Solution by Central Valley Math Circle (Goes through full thought process)== | ||
https://youtu.be/-XcShDyuZIo | https://youtu.be/-XcShDyuZIo | ||
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==Video Solution 2 (MATH-X)== | ==Video Solution 2 (MATH-X)== | ||
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https://youtu.be/5ZIFnqymdDQ?si=IbHepN2ytt7N23pl&t=53 | https://youtu.be/5ZIFnqymdDQ?si=IbHepN2ytt7N23pl&t=53 | ||
− | + | ==Video Solution 4 (Quick and Easy)== | |
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− | ==Video Solution 4 (Quick and Easy | ||
https://youtu.be/Ol1seWX0xHY | https://youtu.be/Ol1seWX0xHY | ||
− | + | ==Video Solution 5 Interstigation== | |
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− | ==Video Solution | ||
https://youtu.be/ktzijuZtDas&t=36 | https://youtu.be/ktzijuZtDas&t=36 | ||
− | ==Video Solution | + | ==Video Solution 6 Daily Dose of Math== |
https://youtu.be/bSPWqeNO11M?si=HIzlxPjMfvGM5lxR | https://youtu.be/bSPWqeNO11M?si=HIzlxPjMfvGM5lxR | ||
− | + | ==Video Solution 7 Dr. David== | |
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− | ==Video Solution | ||
https://youtu.be/RzPadkHd3Yc | https://youtu.be/RzPadkHd3Yc | ||
− | ==Video Solution | + | ==Video Solution 8 WhyMath== |
https://youtu.be/i4mcj3jRTxM | https://youtu.be/i4mcj3jRTxM | ||
Revision as of 16:37, 13 January 2025
Contents
[hide]- 1 Problem
- 2 Solution 1
- 3 Solution 2
- 4 Solution 3
- 5 Solution 4
- 6 Solution 5
- 7 Video Solution 1 (Detailed Explanation)
- 8 Video Solution by Central Valley Math Circle (Goes through full thought process)
- 9 Video Solution 2 (MATH-X)
- 10 Video Solution 3 (A Clever Explanation You’ll Get Instantly)
- 11 Video Solution 4 (Quick and Easy)
- 12 Video Solution 5 Interstigation
- 13 Video Solution 6 Daily Dose of Math
- 14 Video Solution 7 Dr. David
- 15 Video Solution 8 WhyMath
- 16 See Also
Problem
What is the ones digit of:
Solution 1
We can rewrite the expression as . We note that the units digit of is because all the units digits of the five numbers are and , which has a units digit of . Now, we have something with a units digit of subtracted from , and so the units digit of this expression is .
Solution 2
So our answer is .
Solution 3
We only care about the units digits. Thus, ends in , after regrouping(10-2) ends in , ends in , ends in , and ends in .
Solution 4
We just take the units digit of each and subtract, adding an extra ten to the first number so we don't get a negative number:
Solution 5
Video Solution 1 (Detailed Explanation)
Video Solution by Central Valley Math Circle (Goes through full thought process)
Video Solution 2 (MATH-X)
https://youtu.be/BaE00H2SHQM?si=O0O0g7qq9AbhQN9I&t=130
Video Solution 3 (A Clever Explanation You’ll Get Instantly)
https://youtu.be/5ZIFnqymdDQ?si=IbHepN2ytt7N23pl&t=53
Video Solution 4 (Quick and Easy)
Video Solution 5 Interstigation
https://youtu.be/ktzijuZtDas&t=36
Video Solution 6 Daily Dose of Math
https://youtu.be/bSPWqeNO11M?si=HIzlxPjMfvGM5lxR
Video Solution 7 Dr. David
Video Solution 8 WhyMath
See Also
2024 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
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 AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.