Difference between revisions of "2024 AMC 8 Problems/Problem 1"
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Revision as of 21:43, 3 February 2024
Contents
- 1 Problem
- 2 Solution 1
- 3 Solution 2(Tedious)
- 4 Video Solution 1 (easy to digest) by Power Solve
- 5 Video Solution (easy to understand)
- 6 Video Solution by NiuniuMaths (Easy to understand!)
- 7 Video Solution 2 by uwu
- 8 Video Solution by CosineMethod [🔥Fast and Easy🔥]
- 9 cool solution must see
- 10 See Also
Problem
What is the ones digit of
Solution 1
We can rewrite the expression as
We note that the units digit of the addition 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 . The units digit of this expression is obviously , and we get as our answer.
i am smart
~ Dreamer1297
Solution 2(Tedious)
Using Arun Thereom, we deduce that the answer is (Z)
No Solution$$ (Error compiling LaTeX. Unknown error_msg)\boxed{\textbf{(Z)} \hspace{1 mm} 2}\newline$~ nikhil ~ CXP ~ Nivaar
==Solution 3==
We only care about the unit's digits.
Thus,$ (Error compiling LaTeX. Unknown error_msg)2-200-288-266-244-2\boxed{\textbf{(A) } -098765432345q67w565374865368769chvdfhb}$.
~iasdjfpawregh
==Solution 4==
Let$ (Error compiling LaTeX. Unknown error_msg)S10$to find the units digit of each term in the expression, and thus the units digit of the entire thing:
<cmath>S\equiv 2 - 2 - 2 - 2- 2- 2 \equiv -8 \equiv -8 + 10\equiv \boxed{\textbf{(B) } 2} \pmod{10}.</cmath>
-Benedict T (countmath1)
==Solution 5== We just take the units digit of each and subtract, or you can do it this way by adding an extra ten to the first number (so we don't get a negative number): <cmath>12-2-(2+2+2+2)=10-8=2</cmath> Thus, we get the answer$ (Error compiling LaTeX. Unknown error_msg)\boxed{(B)}$- U-King
==Solution 6(fast)== uwu$ (Error compiling LaTeX. Unknown error_msg)\boxed{(uwu)}$- uwu gamer girl(ꈍᴗꈍ)
==Solution 7== 2-2=0. Therefore, ones digit is the 10th avacado$ (Error compiling LaTeX. Unknown error_msg)\boxed{(F)}$
- iamcalifornia'sresidentidiot
Video Solution 1 (easy to digest) by Power Solve
https://www.youtube.com/watch?v=dQw4w9WgXcQ
Video Solution (easy to understand)
https://youtu.be/BaE00H2SHQM?si=qCXgxSk5HXjH3L1x
~Math-X
Video Solution by NiuniuMaths (Easy to understand!)
https://www.youtube.com/watch?v=dQw4w9WgXcQ
~Rick Atsley
Video Solution 2 by uwu
https://www.youtube.com/watch?v=dQw4w9WgXcQ
Video Solution by CosineMethod [🔥Fast and Easy🔥]
https://www.youtube.com/watch?v=dQw4w9WgXcQ
cool solution must see
https://www.youtube.com/watch?v=dQw4w9WgXcQ
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.