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
- Candles are lit at minutes 0, 10, 20, 30, 40 and 50.
- Each lasts 40 minutes, so the one lit at minute t is out by minute t+40.
- 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.
- That leaves 4 candles burning.
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