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myfish Rising GMAT Star Default Avatar
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NEW GMATPrep CAT question Post Fri May 11, 2012 3:00 pm
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  • Lap #[LAPCOUNT] ([LAPTIME])
    In the xy-plane, at what two points does the graph of y=(x+a)(x+b) intersect the x-axis?

    (1) a+b=-1
    (2) the graph intersects the y-axis at (0,-6)

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    mathbyvemuri Really wants to Beat The GMAT! Default Avatar
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    Post Fri May 11, 2012 8:17 pm
    y = (x+a)(x+b)
    To find the points of intersection with X-axis, substitute y=0,which is the equation of X-axis, in the given equation.
    (x+a)(x+b)=0
    x = -a or -b.
    So, (-a,0) and (-b,0) are the points of intersection on X-axis. (as y-coordinates are obviously zero)
    So, the problem is to find a and b values.
    statement(1)=> gives only one equation in a and b and hence not sufficient to get a and b
    statement(2)=>point of intersection on Y-axis is given (0,-6)
    To find the points of intersection on Y-axis, substitute x=0,which is the equation of Y-axis, in the given equation.
    y = ab
    but the point of intersection is given as (0,-6) => y = -6 = ab
    => this gives a new relation between a and b, which when taken together with statement(1),resolves values of a and b
    Answer"C"



    Last edited by mathbyvemuri on Fri May 11, 2012 8:44 pm; edited 1 time in total

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    Post Fri May 11, 2012 8:42 pm
    myfish wrote:
    In the xy-plane, at what two points does the graph of y=(x+a)(x+b) intersect the x-axis?

    (1) a+b=-1
    (2) the graph intersects the y-axis at (0,-6)
    Given: y = (x + a)(x + b)
    Implies the graph intersects x-axis at x = -a or x = -b.
    Thus we have to find the values of a and b.

    Statement 1: (a + b) = -1
    Infinite numbers of values are possible for a and b.

    Not sufficient.

    Statement 2: The graph intersects y-axis at (0, -6)
    For x = 0, y = (0 + a)(0 + b) = ab = -6
    Infinite numbers of values are possible for a and b.

    Not sufficient.

    1 and 2 Together: (a + b) = -1 and ab = -6
    Now, (a - b)² = (a + b)² - 4ab = (-1)² - 4*(-6) = 25
    => (a - b) = ±5

    Thus, either (a = 2, b = -3) or (a = -3, b = 2)
    In both of the cases the graph intersects x-axis at x = -3 and x = 2.

    Sufficient.

    The correct answer is C.

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