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kaplan 800 question

This topic has 1 expert reply and 3 member replies
kandelaki Senior | Next Rank: 100 Posts Default Avatar
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Posted:
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kaplan 800 question

Post Thu Feb 22, 2007 10:54 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    if -1/2<or equal to x<or equal to-1/3
    and -1/4<or equal to y< or equal to -1/5


    which is the minimum value of xy^2 ?

    choices
    -1/75
    -1/50
    -1/48
    -1/32
    -1/16

    the explanation says that the minimum value means farthest from 0. thats true , yes. however i believe farthest from 0 we achive by taking lowest possibilies of x and y ( that is 1/3 form x and 1/5 from y) and get -1/75 as answerr
    but the official answer they took was 1/2 and 1/4 and got -1/32
    i am all confused here

    please help

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    banona Senior | Next Rank: 100 Posts Default Avatar
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    Post Fri Feb 23, 2007 2:56 pm
    Hi,
    Personnally, when manipulating inequatlities of negative numbers I convet them to inequalties of positive numbers to make them regular and easy to treat;

    Fo this one,I would take the positive number (-x) which would be 1/3 < -x < 1/2

    I would consider y^2 as the same of (-y)^2 and get,
    1/25 < y^2 < 1/16 as 1/5 <-y < 1/4

    then, the product -xy^2 as a positive number, would fit the following inequality : 1/75 < -xy^2 < 1/32

    Now, it's easy to get xy^2 inequality as follows:

    -1/32 < xy^2< -1/75


    it's then obvious that the minimum value of xy^2 is -1/32

    I hope I am right

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    jayhawk2001 Community Manager
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    Post Sat Feb 24, 2007 8:54 am
    For min and max values question, it is important to know the sign of
    the end-result.

    In this case, we know that the xy^2 will be negative. So, minimum
    value of xy^2 will have to be a number which is farther away from zero.
    (A simple example would be to compare -1 and -3, -3 is the minimum since it is farther away from 0 compared to -1.)

    So, min (xy^2) is in essence min (x) * max (y^2) which yields
    -1/2 * 1/16 = -1/32. Please note that we can split min (xy^2) as
    above only because we already know what the sign of the
    end result will be.

    GMAT/MBA Expert

    Stacey Koprince GMAT Instructor
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    Post Mon Feb 26, 2007 11:00 pm
    Also, just FYI - this might be what is messing you up:

    -75 is further from zero than -32.

    BUT -1/75 is closer to zero than -1/32.

    Think about two fractions that are much easier to understand: -1/2 and -1/3. Which one is closer to zero? -1/3. And that has the larger number in the denominator.

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    kandelaki Senior | Next Rank: 100 Posts Default Avatar
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    Post Tue Feb 27, 2007 2:47 am
    Oh, Surprised now i get it! thanks Stacey!!

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