2024 AMC 8 Problems/Problem 1

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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.