2025 AMC 8 Problems/Problem 6
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[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?
A)15 B)16 C)17 D)18 E)19
Solution 1
First, we sum the numbers to get
. The number subtracted therefore must be 1 more than a multiple of 4. Thus, the answer is
.
~Gavin_Deng
Solution 2
We consider modulo . The sum of the residues of these numbers modulo
is
. Hence, the number being subtracted must be congruent to
modulo
. The only such number here is
. ~cxsmi
Solution 3
, subtracting the first option gives
, the largest mutliple of 4 less or equal to
is
,
.
~ alwaysgonnagiveyouup