2024 AMC 8 Problems/Problem 1
Contents
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.
~ Dreamer1297
Solution 2
This means the ones digit is
~ nikhil
~ CXP
Solution 3
We only care about the unit's digits.
Thus, ends in
,
ends in
,
ends in
,
ends in
, and
ends in
.
~MrThinker
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)
Video Solution 1 (easy to digest) by Power Solve
https://www.youtube.com/watch?v=HE7JjZQ6xCk
Video Solution 2 by SpreadTheMathLove
https://www.youtube.com/watch?v=L83DxusGkSY
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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