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Math Help - trick to solve?

  1. #1
    Senior Member sfspitfire23's Avatar
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    trick to solve?

    Hey guys,

    I'm studying for the gre and am wondering if there's any trick to solving a problem like this w/o doing the actual math:

    Which is greater:

    210,000 X 95,250

    or

    210,250 X 95,000


    What is the general trick?

    Thanks!
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  2. #2
    A Plied Mathematician
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    Hmm. Generally, I'd say that you're looking at an extremum problem, essentially. You're looking at the product of two numbers, x * y, such that x + y = const. It's like maximizing the area of a rectangle given that the perimeter is constant. What's your gut instinct?
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  3. #3
    Senior Member
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    well if you imagine 210,000 x 95250 as 210000 x (95000+250) = 210000 x 95000 + 210000 x 250 and
    210250 x 95000 as 95000 x (210000+250) = 210000 x 95000 + 95000 x 250 the answer should become obvious?
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  4. #4
    Super Member

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    Hello, sfspitfire23!

    Which is greater: .[1] 210,000 95,250 .or .[2] 210,250 95,000 ?

    We have:

    [1] (210,000) (95,000 + 250) . and .[2] (210,000 + 250) (95,000)


    Let: .x = 210,000, .y = 95,000


    Then we have: .x(y+250) .[?] .(x+250)y

    . . . . . . . . . . . xy + 250x .[?] .xy + 250y

    . . . . . . . . . . . . . . .250x .[?] .250y

    . . . . . . . . . . . . . . . . . x .[?] .y


    Since x > y, then: .[1] .> .[2]
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