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Math Help - help!

  1. #1
    Junior Member
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    help!

    hi guys, could you please help with this problem?



    Is xy>0?

    1) x-y>-2

    2) x-2y<-6

    Choose among the 5 possibilities:
    A) STATEMENT 1 ALONE IS SUFFICIENT
    B) STATEMENT 2 ALONE IS SUFFICIENT
    C) THE 2 STATEMENTS TOGETHER ARE SUFFICIENT
    D) EACH STATEMENT ALONE IS SUFFICIENT
    E) THE 2 STATEMENTS TOGETHER ARE NOT SUFFICIENT



    The textbook I'm practicing on gives C) as the answer, but I cannot figure it out. Could you please explain the right solving sequence?
    thank you
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by simone View Post
    hi guys, could you please help with this problem?



    Is xy>0?

    1) x-y>-2

    2) x-2y<-6

    Choose among the 5 possibilities:
    A) STATEMENT 1 ALONE IS SUFFICIENT
    B) STATEMENT 2 ALONE IS SUFFICIENT
    C) THE 2 STATEMENTS TOGETHER ARE SUFFICIENT
    D) EACH STATEMENT ALONE IS SUFFICIENT
    E) THE 2 STATEMENTS TOGETHER ARE NOT SUFFICIENT



    The textbook I'm practicing on gives C) as the answer, but I cannot figure it out. Could you please explain the right solving sequence?
    thank you
    You have the condition xy > 0

    So consider:
    x - y > -2

    -y > -x - 2

    y < x + 2

    So if x = 1 then y could certainly be -10. Thus we can't say xy > 0.

    Let's try the second one:
    x - 2y < -6

    -2y < -x - 6

    y > \frac{x}{2} + 3

    Here, even if y is positive, x could well be negative. (Try x = -1, y = 10).

    So neither condition by itself will guarentee that xy > 0

    What about together? The easiest way to see this is to graph it. (See below.) Where the shaded regions overlap is the solution to the combined inequalities and is a region where both x and y are positive. Thus we have a requirement that xy > 0, so both conditions are required and sufficient.

    -Dan
    Attached Thumbnails Attached Thumbnails help!-inequalities.jpg  
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  3. #3
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    a big big big thank you , I'm sorry for double posting.
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