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For a trade show, two different cars are selected

This topic has 1 expert reply and 0 member replies

For a trade show, two different cars are selected

Post Wed Nov 08, 2017 7:59 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    For a trade show, two different cars are selected randomly from a lot of 20 cars. If all the cars on the lot are either sedans or convertibles, is the probability that both cars selected will be sedans greater than 3/4?

    1) At least three-fourths of the cars are sedans.
    2) The probability that both of the cars selected will be convertibles is less than 1/20.

    The OA is E .

    Experts, can you help me. I don't have it clear.

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Wed Nov 08, 2017 6:27 pm
    Hi VJesus12,

    We're told that two different cars are selected randomly from a lot of 20 cars (and that all of the cars are either sedans or convertibles). We're asked if the probability that BOTH cars selected will be sedans is greater than 3/4. This is a YES/NO question. We can solve it by TESTing VALUES.

    1) At least three-fourths of the cars are sedans.

    IF... there are 15 sedans and 5 convertibles, then the probability of selecting 2 sedans is....
    (15/20)(14/19) = (3/4)(14/19)
    You don't have to actually calculate this value, since we're multiplying 3/4 by a positive fraction, the answer will be LESS then 3/4 and the answer to the question is NO.

    IF... there are 19 sedans and 1 convertible, then the probability of selecting 2 sedans is....
    (19/20)(18/19) = 18/20 = 90% and the answer to the question is YES.
    Fact 1 is INSUFFICIENT

    2) The probability that both of the cars selected will be convertibles is less than 1/20.

    IF... there are 15 sedans and 5 convertibles, then the probability of selecting 2 convertibles is....
    (5/20)(4/19) = 1/19.... This is NOT a match for the information in Fact 2 though, so there MUST BE FEWER than 5 convertibles.

    IF... there are 16 sedans and 4 convertibles, then the probability of selecting 2 convertibles is....
    (4/20)(3/19) = 3/95
    The probability of selecting 2 sedans under these circumstances is...
    (16/20)(15/19) = (15/20)(16/19) - since we're multiplying 3/4 by a positive fraction, the answer will be LESS then 3/4 and the answer to the question is NO.

    IF... there are 19 sedans and 1 convertible, then the probability of selecting 2 sedans is....
    (19/20)(18/19) = 18/20 = 90% and the answer to the question is YES.
    Fact 2 is INSUFFICIENT

    Combined, we know that there must be FEWER than 5 convertibles. From the work that we did in Fact 2 (above), we have proof that the answer could be NO (if there are 4 convertibles) and YES (if there is just 1 convertible).
    Combined, INSUFFICIENT

    Final Answer: E

    GMAT assassins aren't born, they're made,
    Rich

    _________________
    Contact Rich at Rich.C@empowergmat.com

    Thanked by: VJesus12

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