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# gmatprept1q19

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Director
Joined: 23 May 2008
Posts: 760

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20 Jun 2009, 17:51
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Joined: 03 Aug 2006
Posts: 112

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20 Jun 2009, 19:31

Asking at what two points does the graph of $$y = (x+a)(x+b)$$ intersect the x-axis?
i.e. when x=? when y=0.

$$\Rightarrow (x+a)(x+b) = 0$$

$$\Rightarrow x(x+b)+a(x+b) = 0$$

$$\Rightarrow x^2 + xb+ ax + ab = 0$$

$$\Rightarrow x^2 + x(a+b) + ab = 0$$

We need to know $$a+b=?$$ and $$ab=?$$ to answer the question.

Looking at Statement 1

$$1. a+b=-1$$

$$\Rightarrow x^2 + (-1)x + ab = 0$$

we still don't know $$ab=?$$

Hence Insufficient.

2. The graph intersects the x-axis at (0,-6)

i.e when x=0, y=-6

$$y = (x+a)(x+b)$$

$$\Rightarrow -6 = (0+a)(0+b)$$

$$\Rightarrow -6 = ab$$

Plugging in this value into

$$x^2 + x(a+b) + ab = 0$$

$$\Rightarrow x^2 + x(a+b) - 6 = 0$$

We are now missing the value for $$(a+b)$$

Hence Insufficient

Looking at Statement 1 and 2 together gives us

$$(a+b)=-1$$ and $$ab=-6$$

Plugging into

$$x^2 + x(a+b) + ab = 0$$

$$\Rightarrow x^2 - x - 6 = 0$$

We can now solve for x. Hence both statements together are sufficient. The answer is C
Re: gmatprept1q19   [#permalink] 20 Jun 2009, 19:31
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