AMC 8 · 2025 · #6
Grade 4 number-theoryPick an answer.
AMC 8 2025 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
There are only five candidates — the five answer choices themselves. That is a textbook setup for Tool #3 (Eliminate Possibilities): test each choice against the rule "sum of the remaining four is a multiple of 4" and keep the one that survives. Tool #2 (Systematic List) keeps the bookkeeping tidy: first compute the total once, then list "85 minus each candidate" in order so no case is missed or double-counted. We deliberately avoid Tool #13 (Algebra) or modular-arithmetic shortcuts — they work, but a 4th-grader can solve this with addition and a divisibility check, which is the whole point.
Add all five numbers once — pairing the ends keeps it easy — and the total comes to 85.
Adding five two-digit numbers is exactly the Grade 4 "fluently add multi-digit whole numbers" skill — no shortcut needed.
4.NBT.B.4Make A Systematic ListErase x and the leftover sum is 85 - x; list that value in order for all five choices so none is missed.
A clean ordered list of five subtractions makes sure no candidate is skipped — same Grade 4 add/subtract fluency.
4.NBT.B.4Make A Systematic ListCheck each leftover sum for divisibility by 4: only 68 passes, so every choice but (C) is eliminated.
Checking whether a number is a multiple of 4 is exactly the Grade 4 "factors and multiples" skill — count by 4s or divide and look for remainder 0.
4.OA.B.4Eliminate PossibilitiesThe lone survivor is 17, so that is the number Sekou erased and the answer is (C).
Tool #3 says: when exactly one choice survives every test, that is the answer.
4.OA.B.4Eliminate PossibilitiesThis AMC 8 problem only needs Grade 4 addition and multiples-of-4 checking you already know!