Probability question

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Probability question

by Mo2men » Sat Apr 01, 2017 6:12 pm
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.

Source: Princeton Review

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by GMATGuruNY » Sun Apr 02, 2017 3:39 am
Mo2men wrote: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.

Source: Princeton Review
Organize the data in a DOUBLE-MATRIX.

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

The following matrix is yielded:
Image

Question stem, rephrased:
What is the value of unscented/total?

Statement 1: If a candle is scented, it has an 80% chance of being round.
The following matrix is yielded:
Image
No way to determine the value of unscented/total.
INSUFFICIENT.

Statement 2: If a candle is square, it has a 25% chance of being scented.
Thus, 1/4 of the 40 square candles -- in other words, 10 candles -- are both square and scented.
The following matrix is yielded:
Image
No way to determine the value of unscented/total.
INSUFFICIENT.

Statements combined:
The following matrix is yielded:
Image
The top of the middle column implies the following:
0.2x = 10
x = 50.

The following matrix is yielded:
Image
Thus, unscented/total = 50/100.
SUFFICIENT.

The correct answer is C.
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by Brent@GMATPrepNow » Sun Apr 02, 2017 4:46 am
I'd like to point out that Mitch's "Double Matrix" approach can be used for most questions featuring a population in which each member has two characteristics associated with it.

Here, we have a population of candles, and the two characteristics are:
- scented or unscented
- round or square

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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