1999 AMC 8 Problem 3: Solution

Work through 1999 AMC 8 Problem 3 on fractions and decimals with a written solution, hints, and a visual explanation.

AlgebraLevel 1 · Warmup

Which triplet of numbers has a sum NOT equal to 1?

  • A. (1/2, 1/3, 1/6)
  • B. (2, −2, 1)
  • C. (0.1, 0.3, 0.6)
  • D. (1.1, −2.1, 1.0)
  • E. (−3/2, −5/2, 5)
Hints
  1. List all five triplets
  2. Check the easy sums
  3. Check choice D
Read the step-by-step solution

Answer: D · (1.1, −2.1, 1.0)

  1. List all five triplets

    Five candidate triplets, each needing to be checked against a sum of 1.

    which one is NOT 1?

  2. Check the easy sums

    Choices A, B, and C each add to 1.

    1/2 + 1/3 + 1/6 = 1; 2 − 2 + 1 = 1; 0.1 + 0.3 + 0.6 = 1

  3. Check choice D

    Add the numbers in choice D.

    1.1 − 2.1 + 1.0 = 0

  4. Check choice E too

    Choice E also sums to 1, confirming D is the only one that differs.

    −3/2 − 5/2 + 5 = 1

  5. Conclude

    Choice D has sum 0, not 1. Therefore the answer is D.

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