2025 AMC 8 Problems/Problem 6
Contents
[hide]Problem
Sekou writes the numbers After he erases one of his numbers, the sum of the remaining four numbers is a multiple of
Which number did he erase?
Solution 1
The sum of all five numbers is . Since
is
more than a multiple of
, the number being subtracted must be
more than a multiple of
. Thus, the answer is
.
~Gavin_Deng
Solution 2
The sum of the residues of these numbers modulo is
. Hence, the number being subtracted must be congruent to
modulo
. The only such answer is
.
~cxsmi
Solution 3
We try out every number using brute force and get .
Note that this is not practical and it is very time-consuming.
Video Solution 1 by Cool Math Problems
https://youtu.be/BRnILzqVwHk?si=1KwyuFBUDqdMtC6t&t=2
Video Solution 2 by SpreadTheMathLove
https://www.youtube.com/watch?v=jTTcscvcQmI
Video Solution 3
Video Solution 4 by Thinking Feet
Video Solution 5 by Daily Dose of Math
See Also
2025 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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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