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Difficult Math Problem #91 - Range

This topic has 1 expert reply and 5 member replies
800guy Master | Next Rank: 500 Posts Default Avatar
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Difficult Math Problem #91 - Range

Post Mon Jan 29, 2007 9:24 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    if -2=<x=<2 and 3<=y<=8, which of the following represents the range of all possible values of y-x?

    (A) 5<=y-x<=6
    (B) 1<=y-x<=5
    (C) 1<=y-x<=6
    (D) 1<=y-x<=10
    (E) 1<=y-x<=10


    from diff math problems doc. OA coming when some people provide answers/explanations

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    jayhawk2001 Community Manager
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    Post Mon Jan 29, 2007 10:44 pm
    Min y-x = min y - max x = 3-2 = 1
    Max y-x = max y - min x = 8-(-2) = 10

    So range seems to be 1 through 10.

    I can't make out the difference between options D and E though.

    800guy Master | Next Rank: 500 Posts Default Avatar
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    Post Wed Jan 31, 2007 9:09 pm
    here's the OA:

    you can easily solve this by subtracting the two inequalities. To do this they need to be in the opposite direction; when you subtract them preserve the sign of the inequality from which you are subtracting.

    3 < y < 8
    multiply the second one by (-1) to reverse the sign
    2 > x > -2
    Subtract them to get
    3 - 2 < y - x < 8 - (-2)
    1 < y - x < 10

    gmatguru Newbie | Next Rank: 10 Posts Default Avatar
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    Post Sun Feb 04, 2007 12:39 am
    Hey can anyone tell me wht is this difficult maths doc?

    800guy Master | Next Rank: 500 Posts Default Avatar
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    Post Mon Feb 05, 2007 2:49 pm
    gmatguru wrote:
    Hey can anyone tell me wht is this difficult maths doc?
    hi guru, you can find it on the gmat resource wiki. it's just a word doc with the toughest gmat practice problems

    Post Fri Oct 06, 2017 6:34 pm
    if -2=<x=<2 and 3<=y<=8
    then x = {-2, -1, 0, 1, 2}
    y= {3, 4, 5, 6, 7, 8}
    now to get the range for y-x,
    for a case study, let's consider a smaller set of numbers
    given p= {2,3}
    q= {4,5}
    p-q = {(4-2), (4-3), (5-2), (5-3)
    ={2, 1, 3, 2}
    ={1, 2, 3}
    we can see that the first term '1' is the difference between the least number in set 'q' - the ' maximum' number in set 'p'
    Similarly, we can see that the last term '3' is the difference between the max. number in set 'q' - the ' min.' number in set 'p'

    therefore, applying this into the question given the range is thus,
    = (min 'y' - max 'x') =< y-x =< (max 'y' - min 'x')
    =(3-2) =< y-x=<(8-(-2))
    = 1=< y-x=< 10
    {1=< y-x=< 10}

    Post Fri Oct 06, 2017 7:06 pm
    Here's a similar question to practice with: http://www.beatthegmat.com/xy-t280232.html

    Cheers,
    Brent

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