2024 AMC 8 Problems/Problem 1
Contents
- 1 Problem
- 2 Solution 1
- 3 Solution 2(Tedious)
- 4 Solution 3
- 5 Solution 4
- 6 Solution 5
- 7 Solution 6(fast)
- 8 Solution 7
- 9 Video Solution 1 (easy to digest) by Power Solve
- 10 Video Solution (easy to understand)
- 11 Video Solution by NiuniuMaths (Easy to understand!)
- 12 Video Solution 2 by uwu
- 13 Video Solution by CosineMethod [🔥Fast and Easy🔥]
- 14 cool solution must see
- 15 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)
Note that this solution is not recommended to use during the actual exam. A lot of students this year had implemented this solution and lost a significant amount of time.
~ nikhil
~ CXP
~ Nivaar
Solution 3
We only care about the unit's digits.
Thus, ends in
,
ends in
,
ends in
,
ends in
, and
ends in
.
~iasdjfpawregh
Solution 4
Let be equal to the expression at hand. We reduce each term modulo
to find the units digit of each term in the expression, and thus the units digit of the entire thing:
-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):
Thus, we get the answer
- U-King
Solution 6(fast)
uwu
- uwu gamer girl(ꈍᴗꈍ)
Solution 7
2-2=0. Therefore, ones digit is the 10th avacado
- 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=_8lhp8-dzNxZ-eUQ
~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.