2025 AMC 8 Problems/Problem 6

Problem

Sekou writes the numbers $15, 16, 17, 18, 19.$ After he erases one of his numbers, the sum of the remaining four numbers is a multiple of $4.$ Which number did he erase?

A)15 B)16 C)17 D)18 E)19

Solution 1

First, we sum the $5$ numbers to get $85$ . The number subtracted therefore must be 1 more than a multiple of 4. Thus, the answer is $\boxed{\textbf{(C)}~17}$ . ~Gavin_Deng

Solution 2

We consider modulo $4$ . The sum of the residues of these numbers modulo $4$ is $-1+0+1+2+3=5 \equiv 1 \pmod 4$ . Hence, the number being subtracted must be congruent to $1$ modulo $4$ . The only such number here is $\boxed{\textbf{(C)}~17}$ . ~cxsmi

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2025 AMC 8 Problems/Problem 6

Problem

Solution 1

Solution 2