Problem 3 · 1999 AMC 8
Easy
Fractions, Decimals & Percents
mental-math
Which triplet of numbers has a sum NOT equal to 1?
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Answer: D — (1.1, −2.1, 1.0).
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Hint 1 of 2
The question wants the ODD one out, so you don't need every exact sum — scan for a triplet whose pieces pair up suspiciously. In D, the two positives 1.1 and 1.0 add to 2.1, the very number being subtracted.
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Hint 2 of 2
Look for cancellation before you add: matching a positive and a negative that erase each other tells you the answer faster than full arithmetic.
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Approach: hunt for the cancellation instead of adding all five
- Glance for pieces that cancel. In D, 1.1 + 1.0 = 2.1, exactly the amount subtracted, so 1.1 − 2.1 + 1.0 = 0 — not 1.
- A quick check confirms the rest land on 1 (½ + ⅓ + ⅙ = 1, 2 − 2 + 1 = 1, .1 + .3 + .6 = 1, −1.5 − 2.5 + 5 = 1).
- The odd one out is (1.1, −2.1, 1.0). Why this transfers: on "which is different" problems, scan for the special structure (a perfect cancellation) before grinding every option — the outlier usually announces itself.
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