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2020 Math Kangaroo

Problem 4

Problem 4 · 2020 Math Kangaroo Easy
Logic & Word Problems careful-countingoff-by-one

Ana starts lighting a candle every 10 minutes. Each candle lasts 40 minutes. After 55 minutes, how many candles will be lit?

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Answer: C — 4
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Hint 1 of 2
A candle is only counted at minute 55 if it has been lit but has not yet burned out.
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Hint 2 of 2
Write down when each candle is lit, then cross off any that started more than 40 minutes before minute 55.
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Approach: track which candles are still burning at minute 55
  1. Candles are lit at minutes 0, 10, 20, 30, 40 and 50.
  2. Each lasts 40 minutes, so the one lit at minute t is out by minute t+40.
  3. At minute 55 the candles from 0 (out at 40) and 10 (out at 50) are gone; those from 20, 30, 40 and 50 still burn.
  4. That leaves 4 candles burning.
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