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Math Help - Market Share

  1. #1
    Junior Member Robocop's Avatar
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    Market Share

    The two pie-charts show the market share of different companies which produces TV and Refrigerator(both) in the first quarter of 2014-15:
    Market Share-pie-charts.jpg

    Which of the following cannot be deducted from the given data:

    (a) The angular difference samsung TV and Electrolux refrigerator is 3.6 degrees.

    (b) Sony is the market leader in the TV and Refrigerator segment combined

    (c) For every 100 dollar turnover of Whirlpool Refrigerator , the difference in the turnover of Electrolux and Samsung Refrigerator is $333.4 million

    (d) None of the above.
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    Junior Member SPOCK's Avatar
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    Re: Market Share

    I think it's (d), though we have to see what other members say about it.
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    Re: Market Share

    Was that really the given question? I would have to say that "there is no such thing as the 'angular distance' between a television and a refrigerator'!
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    Junior Member Robocop's Avatar
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    Re: Market Share

    Quote Originally Posted by HallsofIvy View Post
    Was that really the given question? I would have to say that "there is no such thing as the 'angular distance' between a television and a refrigerator'!
    (a)(13-12)=1%=3.6 degrees.Of course it would be the angular distance between the market share as depicted by the pie-charts.

    The official answer to this question is (b), which I don't know how to derive. Request advise for the solution.
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    Re: Market Share

    Although there is no scale given, i.e. in $1M or in $K or in percent or ..., the assumption would be (at least by me) that the numbers were percent. Not only would that make (a) makes sense and make (a) and (B) true but the numbers for both pie charts add to 100. Thus we have no numbers for actual monetary values and (almost) anything said involving this would not be deducible from the charts, i.e. (c) is the answer.

    If the answer is actually (b), what do the numbers mean?
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    Junior Member SPOCK's Avatar
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    Re: Market Share

    Hello Robocop,

    Are you serious the ans is (b). Even if we assume that the numbers given are percentages, all the options can be deduced. So in my opinion the ans should be (d). Please check your source.
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    Re: Market Share

    Quote Originally Posted by SPOCK View Post
    Hello Robocop,

    Are you serious the ans is (b). Even if we assume that the numbers given are percentages, all the options can be deduced. So in my opinion the ans should be (d). Please check your source.
    Please, what is your reasoning for saying (c) is true? Assuming percentages, I get Whirlpool is .06 T where T is the Total turnover in Refrigerators. The difference between Electrolux and Samsung Refrigerator is (.13 - .11) T = 0.02 T. The ratio (Whirlpool/difference) is 2 so for every $100 turnover for Whirlpool, there is a $50 difference in the turnover between Electrolux and Samsung Refrigerator not a 333400000 dollar turnover.
    Last edited by Ishuda; August 12th 2014 at 08:50 AM.
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    Junior Member Robocop's Avatar
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    Re: Market Share

    Hi guys,

    Yes , the numbers are percentages and I agree with Ishuda and Spock the answer cannot be (b). Let me give the answers as given in the book:

    (b)We don't know the turnover of TV and Refrigerator market for each brand. Hence (b) cannot be inferred.

    (c) 6% of total refrigerator market= 1000 million
    Total refrigerator market = 16670 million
    Difference=2% of 16670= 333.4 million
    (Regret there was an error in the original post: it's $ 1000 million in option (c))

    Thus, there must be an error in the book. We can clearly see that Sony is the market leader since Sony has the highest percentage of market share in both the segment. So Sony must be the leader. Request an advice on my concept that percentage market share is sufficient to determine the market leader if all the percentages are given.And that the information about turnover as mentioned in the above solution is not required in such case. Please inform soon.
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    Re: Market Share

    Ok - I'm assuming two different things for the problem so I agree the answer is (b) assuming (c) is corrected to show 'the right numbers' and the numbers represent percentages

    For an example, let Refrigerator total be 2M and TV total be 2000M. Hatachi's total of 320.44M would be a lot larger than Sony's total of 300.38M. There's a lot of other numbers where it would work the same way.
    Last edited by Ishuda; August 12th 2014 at 01:09 PM.
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  10. #10
    Junior Member Robocop's Avatar
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    Re: Market Share

    Quote Originally Posted by Ishuda View Post
    Ok - I'm assuming two different things for the problem so I agree the answer is (b) assuming (c) is corrected to show 'the right numbers' and the numbers represent percentages

    For an example, let Refrigerator total be 2M and TV total be 2000M. Hatachi's total of 320.22M would be a lot larger than Sony's total of 300.38M. There's a lot of other numbers where it would work the same way.
    Hi Ishuda,

    Thanks for the explanation. But you got the items in reverse which I have highlighted in red color. The right pie-chart is for Refrigerator and the left pie-chart is for TV. Nevertheless, your explanation was actually very helpful. Therefore, the book is actually correct and the leadership of the market will depend on the total turnover in a particular segment. Can you suggest some more numbers like above where Sony will not be the market leader. Thanks in advance.
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    Re: Market Share

    Let Tt be the total amount of TV's sold, Tr the total amount of Refrigerators, TS the total amount for Sony, and TH the total amount for Hitachi. Also let Tt = A Tr for some positive number A. Then
    TS = 0.19 Tt + 0.15 Tr = (0.19 A + 0.15) Tr
    and
    TH = 0.11 Tt + 0.16 Tr = (0.11 A + 0.16) Tr

    Since, for our counter example to (c), we want TS less than TH, we have
    (0.19 A + 0.15) Tr < (0.11 A + 0.16) Tr
    or
    0.08 A < 0.01
    which implies A is less than 0.125.

    So choose any number for Tr and any positive A less than 0.125 and (c) will be false [that is , if I haven't made a mistake like last two times - thnx btw].
    Last edited by Ishuda; August 13th 2014 at 08:33 AM.
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