Difference between revisions of "2024 AMC 8 Problems/Problem 1"
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+ | ==Video Solution by Interstigation== | ||
+ | https://youtu.be/ktzijuZtDas&t=36 | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2024|before=First Problem|num-a=2}} | {{AMC8 box|year=2024|before=First Problem|num-a=2}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 02:27, 6 February 2024
Contents
[hide]- 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 Video Solution by Interstigation
- 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 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 (B)
Solution 3
We only care about the unit's digits.
Thus, ends in , ends in , ends in , ends in , and ends in .
~iasdjfpawregh ~vockey
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)
This is not useful. Please come up with a proper solution or delete.
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 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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.