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Each candle in a particular box is either round or square

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Each candle in a particular box is either round or square

by Gmat_mission » Sun Jun 30, 2019 8:45 am

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Each candle in a particular box is either round or square and either scented or unscented. If 60% of the candles are round, what is the probability that a candle selected randomly from the box will be unscented?

(1) If a candle is scented, it has an 80% chance of being round.
(2) If a candle is square, it has a 25% chance of being scented.

[spoiler]OA=C[/spoiler]

Source: Princeton Review
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Source: — Data Sufficiency |
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by deloitte247 » Sat Jul 13, 2019 4:32 am

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What is the probability that a candle selected randomly from the box will be unscented.
Statement 1=> if a candle is scented, it has 80% chance of being round, that means 20% will be square.
Let's assume total candle = 100%
Scented round candle = 80% and scented square candle = 20% but no data about % of unscented candles, hence statement 1 is not SUFFICIENT.

Statement 2 => If a candle is square, it has 25% chance of being scented.
From the question, we know that 60% are round and 40% will be square; of the 40 square, 25% are scented so 25% of 40 = 10
i.e 10 scented square and 30 unscented square = 40% total % of scented and unscented candle is not known hence statement 2 is not SUFFICIENT.

Both statement together =>out of 40% square candles 10 are scented [ i.e 20% ] hence total scented = 50 which is 1/2 then total unscented = 100 - 50 = 50
probability of a candle being unscented = 50%

BOTH statement together are SUFFICIENT.
Answer = Option C
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