Each candle in a particular box is either round or square and either scented or unscented. If 60% of the...

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BTGmoderatorLU: Moderator; Posts: 2547; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Fri Apr 03, 2020 3:02 am

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Source: Princeton Review

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.

The OA is C

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Source: Beat The GMAT — Data Sufficiency | Fri Apr 03, 2020 3:02 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

Re: Each candle in a particular box is either round or square and either scented or unscented. If 60% of the...

by deloitte247 » Sun Apr 05, 2020 1:23 pm

Target question: What is the probability that a candle selected randomly from the box will be unscented?
Given that 60% of the candles are round; therefore, 40% of the candles must be square.

Statement 1: If a candle is scented, it has an 80% chance of being round.
If 80% of scented candles are round, then, 20% of scented candles are square.
However, the relationship between scented and unscented candles cannot be established because there is no proportionality relating to them. Hence, statement 1 is NOT SUFFICIENT.

Statement 2: If a candle is square, it has a 25% chance of being scented.
25% of square candles are scented
75% of square candles are unscented
Since 40% of candles are square; then,
Scented square candles = 40% of 25% = 0.4 * 25 = 10%
Unscented square candles = 40% of 75% = 0.4 * 75 = 30%
However, the relationship between scented round candles and unscented round candles cannot be established because there is no proportionality relating to them. Hence, statement 2 is NOT SUFFICIENT.

Combining both statements together:
From statement 1, 20% of scented candles are square
From statement 2, total scented square candles = 10%
Therefore, if 20% of scented candles = 10% of square candles; then,
80% of scented candles =
$$\frac{80\cdot10}{20}=40\%\ round\ candles$$
So, total scented candles = 40 + 10 = 50%, and unscented candles = 100 - 50 = 50%
Therefore, the chance of selecting an unscented candle = 50%. Hence, both statements combined together are SUFFICIENT.

Answer = option C

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