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2024 AMC 8 Problems/Problem 1

Revision as of 22:34, 7 February 2024 by Morgansu (talk | contribs) (→‎Solution 7)

Problem

What is the ones digit of\[222,222-22,222-2,222-222-22-2?\]$\textbf{(A) } 0\qquad\textbf{(B) } 2\qquad\textbf{(C) } 4\qquad\textbf{(D) } 6\qquad\textbf{(E) } 8$

Solution 1

We can rewrite the expression as \[222,222-(22,222+2,222+222+22+2).\]

We note that the units digit of the addition is $0$ because all the units digits of the five numbers are $2$ and $5*2=10$, which has a units digit of $0$.

Now, we have something with a units digit of $0$ subtracted from $222,222$. The units digit of this expression is obviously $2$, and we get $\boxed{B}$ as our answer.

i am smart

~ Dreamer1297

Solution 2(Tedious)

Using Arun Thereom, we deduce that the answer is (B)

Solution 3

We only care about the unit's digits.

Thus, $2-2$ ends in $0$, $0-2$ ends in $8$, $8-2$ ends in $6$, $6-2$ ends in $4$, and $4-2$ ends in $\boxed{\textbf{(B) } 2}$.

~iasdjfpawregh ~vockey

Solution 4

Let $S$ be equal to the expression at hand. We reduce each term modulo $10$ to find the units digit of each term in the expression, and thus the units digit of the entire thing:

\[S\equiv 2 - 2 - 2 - 2- 2- 2 \equiv -8 \equiv -8 + 10\equiv \boxed{\textbf{(B) } 2} \pmod{10}.\]

-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): \[12-2-(2+2+2+2)=10-8=2\] Thus, we get the answer $\boxed{(B)}$

- U-King

Solution 6(fast)

uwu $\boxed{(uwu)}$

- uwu gamer girl(ꈍᴗꈍ)

This is not useful. Please come up with a proper solution or delete.

Hello, please remove this nonsense post, or your account will be in risk of banning.

I DONT CARE NOBODY ASKED(ꈍᴗꈍ)

Solution 7

2-2=0. Therefore, ones digit is the 10th avacado $\boxed{(F)}$

- iamcalifornia'sresidentidiot

Hello, please remove this nonsense post, or your account will be in risk of banning

this is not nonsense like what are you yapping about this is the most beautiful solution every to be conceived in all of humanity i literally deserve a nobel prize

PS touch grass

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=_8lhp8-dzNxZ-eUQ

~Math-X

Video Solution by NiuniuMaths (Easy to understand!)

https://www.youtube.com/watch?v=dQw4w9WgXcQ

~Rick Aopsly

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

Video Solution by Interstigation

https://youtu.be/ktzijuZtDas&t=36

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

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