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Probability question

This topic has 2 expert replies and 0 member replies
Mo2men Legendary Member Default Avatar
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Probability question

Post 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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Top Reply
Post 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: http://www.gmatprepnow.com/module/gmat-word-problems?id=919

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

Easy Problem Solving questions
- http://www.beatthegmat.com/finance-majors-non-finance-majors-overlapping-set-question-t167425.html

Medium Problem Solving questions
- http://www.gmatprepnow.com/module/gmat-word-problems/video/920
- http://www.beatthegmat.com/posted-speed-limit-t272374.html
- http://www.beatthegmat.com/motel-t271938.html
- http://www.beatthegmat.com/of-the-applicants-passes-a-certain-test-15-t270255.html
- http://www.beatthegmat.com/opening-night-and-late-patrons-t264869.html
- http://www.beatthegmat.com/at-least-100-students-at-a-certain-high-school-study-japanes-t274669.html
- http://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- http://www.gmatprepnow.com/module/gmat-word-problems/video/946
- http://www.beatthegmat.com/ratio-problem-t268339.html
- http://www.beatthegmat.com/overlapping-sets-question-t265223.html
- http://www.beatthegmat.com/fractions-t264254.html
- http://www.beatthegmat.com/overlapping-sets-t264092.html
- http://www.beatthegmat.com/mba/2011/05/09/random-double-matrix-question-2

Easy Data Sufficiency questions
- http://www.gmatprepnow.com/module/gmat-word-problems/video/943
- http://www.beatthegmat.com/for-what-percent-of-those-tested-for-a-certain-t270596.html
- http://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- http://www.beatthegmat.com/sets-matrix-ds-t271914.html
- http://www.beatthegmat.com/each-of-people-voted-once-in-an-election-x-t271375.html
- http://www.beatthegmat.com/a-manufacturer-t270331.html
- http://www.beatthegmat.com/in-costume-for-halloween-t269355.html
- http://www.beatthegmat.com/mba/2011/05/05/random-double-matrix-question-1

Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- http://www.beatthegmat.com/double-set-matrix-question-t271423.html
- https://youtu.be/dOZ9KM1m5Hs
- http://www.beatthegmat.com/sets-t269449.html
- http://www.beatthegmat.com/mba/2011/05/16/random-double-matrix-question-3

Cheers,
Brent

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Brent Hanneson – Founder of GMATPrepNow.com
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Top Reply
Post 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:
ttps://postimg.org/image/umtnwcmb5/" target="_blank">

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:
ttps://postimg.org/image/cj4av15ez/" target="_blank">
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:
ttps://postimg.org/image/ehycej8tj/" target="_blank">
No way to determine the value of unscented/total.
INSUFFICIENT.

Statements combined:
The following matrix is yielded:
ttps://postimg.org/image/r6z5syrsl/" target="_blank">
The top of the middle column implies the following:
0.2x = 10
x = 50.

The following matrix is yielded:
ttps://postimg.org/image/yt4819un3/" target="_blank">
Thus, unscented/total = 50/100.
SUFFICIENT.

The correct answer is C.

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