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Probability question

This topic has 2 expert replies and 0 member replies

Probability question

Post Sat Apr 01, 2017 6:12 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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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    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:


    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:

    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:

    No way to determine the value of unscented/total.
    INSUFFICIENT.

    Statements combined:
    The following matrix is yielded:

    The top of the middle column implies the following:
    0.2x = 10
    x = 50.

    The following matrix is yielded:

    Thus, unscented/total = 50/100.
    SUFFICIENT.

    The correct answer is C.

    _________________
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    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

    _________________
    Brent Hanneson – Founder of GMATPrepNow.com
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