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gmatprept1q19

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gmatprept1q19 [#permalink] New post 20 Jun 2009, 16:51
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A
B
C
D
E

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(N/A)

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0% (00:00) correct 0% (00:00) wrong based on 0 sessions
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Re: gmatprept1q19 [#permalink] New post 20 Jun 2009, 18:31
The answer is C

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, 18:31
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