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Math Help - Reading from a table of statistics, hard to find the %

  1. #1
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    Reading from a table of statistics, hard to find the %

    Hi all,

    The following is a short problem i'm desperately trying to work out. Here is a table of figures:

    Total Population is 20 million.

    Now, the first question asks: What percentage of the population live in either Tokyo, Yoko or Hiro?
    I can choose from four answers:
    a. 52%
    b. 11.8%
    c. 45%
    d. cannot say

    The answer happens to be b. 11.8%

    How on earth they reach that I have no idea. I have tried the following:
    'Total population' - 'Total Other'
    ie. (0.25+0.45+0.3) - (0.125+0.325+0.2) = 0.35
    or 35%

    but apparently that is not correct and isn't in the list of answers.

    The second question is: How many in the total population do not live in the city's above?

    a. 4,300,000
    b. 4,800,000
    c. 5,100,000
    d. 4,750,000

    The answer is d.

    I have tried 0.65 * 20,000,000 = 13m
    But that is not correct according to the answer given.

    Much needed help. Thanks!
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  2. #2
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    I can help you with the second part.

    20M total in the population.

    .25 are under 30
    (.25)(20M)
    5M people

    .45 are 30-45
    (.45)(20M)
    9M people

    .30 are over 45
    (.30)(20M)
    6M people

    From there you take the number of people from each age group and multiply by the percent of that age group that does not live in Tokyo, Hiro, or Yoko. (the "Other" group on your chart)

    There are 5M people in the population under 30, from the chart we see that .125 of the population under 30 lives outside those three cities.

    under 30 and outside the cities: (.125)(5M)=625,000
    30-45 and outside the cities: (.325)(9M)=2,925,000
    over 45 and outside the cities: (.20)(6M)=1,200,000

    total population not in Tokyo, Hiro or Yoko = 625,000 + 2,925,000 + 1,200,000 = 4,750,000


    the first question I tried twice and I do not understand how they got 11.8% as the answer.
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  3. #3
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    bm203, thanks so much for going through the effort to help me out. I really appreciate it and have given you credit.

    BTW, what answer did you get for Q1? Was it the same as my answer?

    I swear, it happens sometimes, but it's really annoying when the authors of these questions make mistakes in their answers!
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  4. #4
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    well if you look at the chart either you are in Tokyo, Hiro, Yoko.... or you're not

    and if you figure we just said that 4,750,000 out of 20M people live outside those three cities and 4,750,000 is 23.75% of the total population... i mean unless I'm reading the question wrong I would think that leaves the other 76.25% of the population distributed across the cities.
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  5. #5
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    well if i do it the long way (which i was trying to avoid) using a similar process as before

    UNDER 30
    In Tokyo (.025)(5M) = 125,000
    In Yoko (.05)(5M) = 250,000
    In Hiro (.05)(5M) = 250,000
    sum: 625,000

    BETWEEN 30-45
    In Tokyo (.05)(9M) = 450,000
    In Yoko (.05)(9M) = 450,000
    In Hiro (.025)(9M) = 225,000
    sum: 1,125,000

    OVER 45
    In Tokyo (.05)(6M) = 300,000
    In Yoko (.025)(6M) = 150,000
    In Hiro (.025)(6M) = 150,000
    sum: 600,000

    600,000 + 1,125,000 + 625,000 = 2,350,000

    divide by total population: 2,350,000/20M = .1175
    Last edited by bm203; February 9th 2010 at 08:06 PM.
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  6. #6
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    [double post. pls delete]
    Last edited by bboydocument; February 9th 2010 at 08:05 PM.
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  7. #7
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    Ah I see now!
    But that means the answer for Q2 would be 20m - 2.35m = 17.65m?

    I mean it's a stupid problem we have here. Because the answer to Q2 would be the remaining population from Q1?

    As an example for < 30 , because you have:
    For < 30, in cities T,Y,H = 625,000
    And, in other = 625,000

    but hang on a sec... the total fraction of the population for < 30 is 5m! And 626k + 625k does not equal 5m? This is what is confusing between the two questions I think.
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