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posted speed limit

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Ankitaverma Rising GMAT Star Default Avatar
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posted speed limit Post Wed Dec 04, 2013 12:27 pm
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  • Lap #[LAPCOUNT] ([LAPTIME])
    On a certain road 10 percent of the motorists exceed the posted speed limit and receive speeding tickets, but 20 percent of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?
    (A) 10*1/2%
    (B) 12*1/2%
    (C) 15%
    (D) 22%
    (E) 30%

    Q/a-b can someone explain

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    Post Wed Dec 04, 2013 12:29 pm
    Ankitaverma wrote:
    On a certain road 10 percent of the motorists exceed the posted speed limit and receive speeding tickets, but 20 percent of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?
    (A) 10*1/2%
    (B) 12*1/2%
    (C) 15%
    (D) 22%
    (E) 30%

    Q/a-b can someone explain
    We can use the Double Matrix Method to solve this question.

    This technique 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 motorists, and the two characteristics are:
    - speeder (S) or non-speeder (~S)
    - get ticket (T) or not get ticket (~T)

    Aside: To learn more about the Double Matrix Method, watch our free video: http://www.gmatprepnow.com/module/gmat-word-problems?id=919

    Since this question concerns percents (instead of actual values), let's assign a "nice" value to the total number of motorists in this population. Let's say there are 100 motorists.

    So, to begin, our matrix looks like this.


    10 percent of the motorists exceed the posted speed limit and receive speeding tickets
    The top left box is for motorists who speed and receive speeding tickets. So, 10% of the entire population will be in this box.


    20 percent of the motorists who exceed the posted speed limit do not receive speeding tickets.
    The motorists referred to here are those who go in the top right box. Unfortunately, we don't know the total number of speeders, so we can't find 20% of that value.
    So, let's let x = the total number of speeders.


    Now we can deal with this: 20 percent of the motorists who exceed the posted speed limit do not receive speeding tickets.
    In other words, 20% of x will go in the top right box.


    At this point, we know that the sum of the top 2 boxes is x.
    So, we can write: 10 + 0.2x = x (now solve)
    Arrange: 10 = 0.8x
    Divide: 10/0.8 = x
    12.5 = x

    Since x represents the total number of speeders, we know that 12.5 out of 100 motorists speed.
    In other words, 12.5% of motorists speed.
    Answer: B

    ---------------------------------------
    Here are some additional practice questions that can be solved using the Double Matrix Method:
    - http://www.beatthegmat.com/mba/2011/05/05/random-double-matrix-question-1
    - http://www.beatthegmat.com/mba/2011/05/09/random-double-matrix-question-2
    - http://www.beatthegmat.com/mba/2011/05/16/random-double-matrix-question-3
    - http://www.beatthegmat.com/ds-quest-t187706.html
    - http://www.beatthegmat.com/overlapping-sets-questions-t183320.html
    - http://www.beatthegmat.com/finance-majors-non-finance-majors-overlapping-set-question-t167425.html
    - http://www.beatthegmat.com/ds-french-japanese-t222297.html

    Cheers,
    Brent

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    Post Wed Dec 04, 2013 2:42 pm
    Hi Ankitaverma,

    Brent presents a solid way to organize the information in the prompt and figure out the correct answer. Here's another way to organize the information:

    The prompt doesn't give us any numbers to use, so let's TEST Values:

    Let's say there are 100 motorists. From the prompt, we know that some exceeded the speed limit and some didn't…

    X = number of exceeded the speed limit
    (100 - X) = number of did not exceed the speed limit

    We're told that 10% exceeded the speed limit AND got a ticket, so that's 10 people.

    This means that the X people who exceeded the speed limit can be broken into 2 groups: those who got a ticket and those who didn't.

    X = (those who got tickets) + (those who didn't)
    X = 10 + (those who didn't)

    Next, we're told that 20% of the motorists who EXCEEDED THE SPEED LIMIT did not receive tickets. That's the equivalent of .2X

    X = 10 + .2X

    Now, solve for X

    .8X = 10
    X = 12.5

    Final Answer: B

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    Rich

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    Post Thu Dec 05, 2013 3:14 am
    Questions like this require careful reading.

    Let
    M = total number of motorists
    S = total number who speed

    So here is the question reworded for those who don't see it:

    10% of M speed and receive speeding tickets
    20% of S don't receive tickets
    Find S/M * 100%

    Post Thu Dec 05, 2013 4:54 am
    Quote:
    on a certain road 10% of the motorists exceed the posted limit and receive speeding tickets, but 20% of the motorists who exceed the posted speed limit do not receive a speeding ticket. What percent of the motorists on the road exceed the posted speed limit?

    A) 10.5%
    B) 12.5%
    C) 15%
    D) 22%
    E) 30%
    This is an EITHER/OR group problem.
    Every motorist EITHER speeds OR doesn't.
    Every motorist EITHER receives a ticket OR doesn't.
    For an EITHER/OR group problem, we can use a GROUP GRID (also known as a double-matrix) to organize the data:

    In the grid above, the entries in any given row or column must add up to the TOTAL of that row or column.

    Let the motorists who exceed the speed limit = 10.
    The following grid is yielded:


    20% of the motorists who exceed the posted speed limit do not receive a speeding ticket.
    Since 20% of 10 = 2, the following grid is yielded:


    10% of the motorists exceed the posted limit and receive speeding tickets.
    Since the 8 motorists who receive a ticket are 10% of the total number of motorists -- and 8 is 10% of 80 -- the following grid is yielded:


    Thus:
    (exceed the speed limit)/(total number of motorists) = 10/80 = 12.5%.

    The correct answer is B.

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