AMC 8 · 2025 · #6

Grade 4 number-theory
multiplesmodular-arithmeticdivisibility-rules systematic-enumerationmodular-arithmetic ↑ Prerequisites: multi-digit-arithmeticmultiples
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Problem
Sekou wrote down the five consecutive whole numbers 15, 16, 17, 18, 19. He erased exactly one of them, and the four numbers that are left add up to a multiple of 4. Which of the five numbers did he erase?

Pick an answer.

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

AMC 8 2025 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.

How to solve
Strategy Eliminate Possibilities

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.

1STEP 1

Add all five numbers once — pairing the ends keeps it easy — and the total comes to 85.

15 + 16 + 17 + 18 + 19 = 85
2STEP 2

Erase x and the leftover sum is 85 - x; list that value in order for all five choices so none is missed.

(A) 85-15 &= 70 ; (B) 85-16 &= 69 ; (C) 85-17 &= 68 ; (D) 85-18 &= 67 ; (E) 85-19 &= 66
3STEP 3

Check each leftover sum for divisibility by 4: only 68 passes, so every choice but (C) is eliminated.

68 = 4 × 17 ✓ 70, 69, 67, 66 are not multiples of 4
4STEP 4

The lone survivor is 17, so that is the number Sekou erased and the answer is (C).

Erased number = 17 → (C)
Answer
17
Quick sanity check: 68 ÷ 4 = 17 with no remainder, so 68 really is a multiple of 4 and erasing 17 works. Notice also that 85 leaves a remainder of 1 when divided by 4, and among 15, 16, 17, 18, 19 exactly one number (17) also leaves remainder 1. That uniqueness explains why the problem has a single answer.
💡Key takeaway

This AMC 8 problem only needs Grade 4 addition and multiples-of-4 checking you already know!