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Terry holds 12 cards, each of which is red, white, green

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jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
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Posted:
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Terry holds 12 cards, each of which is red, white, green

Post Thu Aug 03, 2017 12:01 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Terry holds 12 cards, each of which is red, white, green, or blue. If a person is to select a card randomly from the cards Terry is holding, is the probability less than 1/2 that the card selected will be either red or white?

    (1) The probability that the person will select a blue card is 1/3
    (2) The probability that the person will select a red card is 1/6

    Official Guide question
    Answer: E

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    Post Thu Aug 03, 2017 1:35 pm
    jjjinapinch wrote:
    Terry holds 12 cards, each of which is red, white, green, or blue. If a person is to select a card randomly from the cards Terry is holding, is the probability less than 1/2 that the card selected will be either red or white?

    (1) The probability that the person will select a blue card is 1/3
    (2) The probability that the person will select a red card is 1/6

    Official Guide question
    Answer: E
    Given: 12 cards - each card is red, white, green, or blue

    Target question: Is the probability less than 1/2 that the card selected will be either red or white?
    This is a good candidate for rephrasing the target question.
    In order for P(selected card is red or white) < 1/2, it must be the case that there are fewer than 6 cards that are either red or white.
    Let R = # of red cards in the deck
    Let W = # of white cards in the deck
    Let G = # of green cards in the deck
    Let B = # of blue cards in the deck
    REPHRASED target question: Is R + W < 6?

    Aside: Here’s a video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100

    Statement 1: The probability that the person will select a blue card is 1/3
    This tells us that B = 4 (since 4/12 = 1/3)
    There are several CONFLICTING scenarios that satisfy statement 1. Here are two:
    Case a: R = 2, W = 1, G = 5 and B = 4. In this case, R + W = 2 + 1 = 3. So, R + W < 6
    Case b: R = 2, W = 6, G = 0 and B = 4. In this case, R + W = 2 + 6 = 8. So, R + W > 6
    Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

    Statement 2: The probability that the person will select a red card is 1/6
    This tells us that R = 2 (since 2/12 = 1/6)
    There are several CONFLICTING scenarios that satisfy statement 2. Here are two:
    Case a: R = 2, W = 1, G = 5 and B = 4. In this case, R + W = 2 + 1 = 3. So, R + W < 6
    Case b: R = 2, W = 6, G = 0 and B = 4. In this case, R + W = 2 + 6 = 8. So, R + W > 6
    Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

    Statements 1 and 2 combined
    IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
    Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

    Answer: E

    Cheers,
    Brent

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