Question

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

$15$

$16$

$17$

$18$

$19$

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Written solution:

The remainders of the five numbers after dividing by $4$ are: $3,$ $0,$ $1,$ $2,$ and $3.$ So, the sum of all five numbers modulo $4$ is the same as $3 + 0 + 1 + 2 + 3 = 9$ which has remainder $1$ modulo $4.$ Therefore, in order to erase a single number and get a sum that is $0$ modulo $4,$ we must erase the number which was $1$ modulo $4,$ which was $17.$ Therefore, the answer is C.

2025 AMC 8 Problem 6

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Problem 6 in Other Years