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Help! Practice Test Gone Wrong

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Help! Practice Test Gone Wrong

by ostrowskiamy » Mon Feb 18, 2013 5:04 pm
Hi folks! I'm close to test date and decided to take one last practice test, just to keep fresh, and...just did way worse on a practice exam than I was expecting. Unfortunately, the correct methodology for reaching solutions to the problems isn't provided on the GMAC practice test I took - I'm seriously hoping someone can help me figure out where I went wrong on these babies, so that I can nail it on test day! I felt pretty confident with all the math "rules" and techniques moving into today, so any clarification would be GREATLY appreciated!

On an xy plane, at what two oints of the graph does y=(x+a)(x+b) intersect x?
(1) a+b = -1
(2) The line intercepts the y axis at (0,-6)

I answered E (because when I foiled the question, I wasn't able to get and b alone so that I could complete the equation for the x intercept) but the answer is C. Why is it C, please?

More questions to follow! Thank you so, so much for any quick assistance!
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by Brent@GMATPrepNow » Mon Feb 18, 2013 6:02 pm
ostrowskiamy wrote:
On an xy plane, at what two points of the graph does y=(x+a)(x+b) intersect x?
(1) a+b = -1
(2) The line intercepts the y axis at (0,-6)

Target question: At what two points of the graph does y=(x+a)(x+b) intersect x?

IMPORTANT: Let's take a close look at the point where a line (or curve) crosses the x-axis. At the point of intersection, the point is on the x-axis, which means that the y-coordinate of that point is 0.

So, for example, to find where the line y=2x+3 crosses the x-axis, we let y=0 and solve for x. We get: 0 = 2x+3
When we solve this for x, we get x= -3/2.
So, the line y=2x+3 crosses the x-axis at (-3/2, 0)


To determine the point where y = (x + a)(x + b) crosses the x axis, let y=0 and solve for x.
We get: 0 = (x + a)(x + b), which means x=-a or x=-b
This means that y = (x + a)(x + b) crosses the x axis at (-a, 0) and (-b, 0)
So, to solve this question, we need the values of a and b

Aside: y = (x + a)(x + b) is actually a parabola. This explains why it crosses the x axis at two points.

Now let's rephrase the target question:
Rephrased target question: What are the values of a and b?

Statement 1: a + b = -1
There's no way we can use this to determine the values of a and b.
Since we can answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The line intercepts the y axis at (0,-6)
This tells us that when x = 0, y = -6
When we plug x = 0 and y = -6 into the equation y = (x + a)(x + b), we get -6 = (0 + a)(0 + b), which tells us that ab=-6
In other words, statement 2 is a fancy way to tell us that ab = -6
Since there's no way we can use this information to determine the values of a and b, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
Statement 1 tells us that a+b = -1
Statement 2 tells us that ab = -6

Rewrite equation 1 as a = -1 - b
Then take equation 2 and replace a with (-1 - b) to get: (-1 - b)(b) = -6
Expand: -b - b^2 = -6
Set equal to zero: b^2 + b - 6 = 0
Factor: (b+3)(b-2) = 0
So, b= -3 or b= 2

When b = -3, a = 2 and when b = 2, a = -3
In both cases, the two points of intersection are (3, 0) and (-2, 0)
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Anurag@Gurome » Mon Feb 18, 2013 11:00 pm
Refer to the posts here << https://www.beatthegmat.com/gmat-prep-li ... tml#304548 >> and here << https://www.beatthegmat.com/gmatprep-i-t ... tml#327945 >>
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