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Does line l have a negative y-intercept?

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Does line l have a negative y-intercept?

by gmattesttaker2 » Sun Nov 24, 2013 3:17 pm
Hello,

Can you please assist with this:

In a coordinate system, point (r, s) is on line l, does line l have a negative y intercept?

(1) r > 0 and s < 0.
(2) Line l has positive slope.

OA: C

Statement 1 is in-sufficient as shown in Line l_1. Statement 2 is in-sufficient as shown in Line l_2. I am not sure though how both are sufficient.

Thanks,
Sri
Attachments
Line l_1.png
Figure_1
Line l_2.png
Figure_2
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by Uva@90 » Mon Nov 25, 2013 7:39 am
Sri,
you came soo close to the solution.
As you are sure that both the statement are not sufficient alone.
Combining 1 and 2:
From the pic,Line l_1 and Line l_2

Only image holds good for both the statements are second graph in Line l_1 and Line l_2.
which says line L has negative Y Intercept.

Regards,
Uva.
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by Brent@GMATPrepNow » Mon Nov 25, 2013 8:03 am
gmattesttaker2 wrote:
In a coordinate system, point (r, s) is on line l, does line l have a negative y intercept?

(1) r > 0 and s < 0.
(2) Line l has positive slope.

Target question: Does line l have a negative y-intercept?

Statement 1: r > 0 and s < 0
We're told that (r,s) is a point on the line.
Statement 1 tells us that r is positive and s is negative.
In other words, the x-coordinate of the given point is positive, and the y-coordinate of the given point is negative.
This means the given point MUST be in the fourth quadrant (where the x-coordinate is positive, and the y-coordinate is negative.)
In other words, the line must pass through the 4th quadrant.
Image

Here are two possible cases:
Image
Image
In one case, the y-intercept is negative, and in the other case, the y-intercept is positive
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Line l has positive slope.
Here are two possible cases:
Image
Image
In one case, the y-intercept is negative, and in the other case, the y-intercept is positive
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
If the line passes through quadrant IV AND the line has a positive slope, the y-intercept is definitely negative
To convince yourself of this, try drawing some lines that satisfy both conditions.
Here are a few:
Image
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 gmattesttaker2 » Thu Nov 28, 2013 12:12 am
Uva@90 wrote:Sri,
you came soo close to the solution.
As you are sure that both the statement are not sufficient alone.
Combining 1 and 2:
From the pic,Line l_1 and Line l_2

Only image holds good for both the statements are second graph in Line l_1 and Line l_2.
which says line L has negative Y Intercept.

Regards,
Uva.
Thanks Uva. Sorry I just missed it. Thanks again for your help. Best Regards - Sri
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by gmattesttaker2 » Thu Nov 28, 2013 12:16 am
Brent@GMATPrepNow wrote:
gmattesttaker2 wrote:
In a coordinate system, point (r, s) is on line l, does line l have a negative y intercept?

(1) r > 0 and s < 0.
(2) Line l has positive slope.

Target question: Does line l have a negative y-intercept?

Statement 1: r > 0 and s < 0
We're told that (r,s) is a point on the line.
Statement 1 tells us that r is positive and s is negative.
In other words, the x-coordinate of the given point is positive, and the y-coordinate of the given point is negative.
This means the given point MUST be in the fourth quadrant (where the x-coordinate is positive, and the y-coordinate is negative.)
In other words, the line must pass through the 4th quadrant.
Image

Here are two possible cases:
Image
Image
In one case, the y-intercept is negative, and in the other case, the y-intercept is positive
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Line l has positive slope.
Here are two possible cases:
Image
Image
In one case, the y-intercept is negative, and in the other case, the y-intercept is positive
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
If the line passes through quadrant IV AND the line has a positive slope, the y-intercept is definitely negative
To convince yourself of this, try drawing some lines that satisfy both conditions.
Here are a few:
Image
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
Hello Brent,

Thanks a lot for the detailed explanation and for the excellent diagrams. It is clear now. Thanks again for your excellent explanations.

Best Regards,
Sri
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