1999 AMC 8 Problem 1: Solution

Work through 1999 AMC 8 Problem 1 on order of operations with a written solution, hints, and a visual explanation.

AlgebraLevel 1 · Warmup

(6 ? 3) + 4 − (2 − 1) = 5. To make this statement true, what operation should replace the question mark between 6 and 3?

  • A. ÷
  • B. ×
  • C. +
  • D. −
  • E. None of these
Hints
  1. Set up the blank
  2. Try all four operations
  3. Watch the trap
Read the step-by-step solution

Answer: A · ÷

  1. Set up the blank

    The expression (6 ? 3) + 4 − (2 − 1) = 5 has one missing operation to find.

    (6 ? 3) + 4 − 1 = 5

  2. Try all four operations

    Plug each of ÷, ×, +, − between 6 and 3.

    6÷3=2, 6×3=18, 6+3=9, 6−3=3

  3. Finish the expression

    Add 4 and subtract 1 for each candidate result.

    2+4−1=5, 18+4−1=21, 9+4−1=12, 3+4−1=6

  4. Watch the trap

    Subtraction gives 6, which is one off from 5 — an easy number to mistake for correct.

    6 ≠ 5

  5. Conclude

    Only division makes the statement true, so the answer is A.

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