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Question Pack 1 difficult geometry

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by fangtray » Thu May 10, 2012 6:12 pm
in the xy-plane, points A, B, and C are not on the same line. Is the slope of BC negative?

1. slope of line AB is -1
2. The measure of angle ABC is 37 degrees
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Source: — Data Sufficiency |
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by mathbyvemuri » Thu May 10, 2012 9:37 pm
IMO "E"
statement(1)=> gives the slope of line AB, which is not sufficient to find the slope of BC
statement(2)=> gives the angle ABC, which is the angle between AB and BC. This alone is not sufficient.
Even if we consider both the statements together, it is not sufficient.
The key concept here is:
"A line is said to have a positive slope if it is inclined upwards from left to right and vice versa"
As the inclination between two lines could be in two ways corresponding to the orientation of one line with the other. line BC can be sloping-up from left to right or just in the reverse way. In both the cases it is possible to make an angle of 37 deg with line AB. So it is just not possible to decide whether the slope is positive or negative.
Last edited by mathbyvemuri on Thu May 10, 2012 9:59 pm, edited 1 time in total.
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by aneesh.kg » Thu May 10, 2012 9:49 pm
It is obvious that both the statements are NOT sufficient independently to determine the nature of the slope of BC.

Let's combine them.
(1)We have a line AB that makes 45 degrees with the negative X-axis but we don't know if A is on the top-left or B is on the top-left.
(2)Then a line BC has to make 37 degrees with AB. In each of the two cases above, BC can be drawn in two directions.

So, there are a total of four cases(as shown in the image below).

Image

[spoiler](C)[/spoiler] is the answer
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by mathbyvemuri » Thu May 10, 2012 10:04 pm
aneesh.kg wrote:It is obvious that both the statements are NOT sufficient independently to determine the nature of the slope of BC.

Let's combine them.
(1)We have a line AB that makes 45 degrees with the negative X-axis but we don't know if A is on the top-left or B is on the top-left.
(2)Then a line BC has to make 37 degrees with AB. In each of the two cases above, BC can be drawn in two directions.

So, there are a total of four cases(as shown in the image below).

Image

[spoiler](C)[/spoiler] is the answer
Kudos Aneesh, great explanation
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by ranjeet75 » Fri May 11, 2012 9:07 am
There is a formula regarding the angle between two lines:

tan�θ=±{(m_2-m_1)/(1+ m_1 m_2 )}

So, one angle and slope of one line is given then we can find the slope of other line.
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by veenitj » Fri May 11, 2012 9:26 am
Didn't understand the explainnation by aneesh.kg. Can you please explani it again in detail. Also I cant see any picture attched to the post.

Thanks in advance.

VJ
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by aneesh.kg » Fri May 11, 2012 10:50 am
You will understand it when you see the image.
Attaching it again:

Image
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by fangtray » Fri May 11, 2012 3:09 pm
aneesh.kg wrote:It is obvious that both the statements are NOT sufficient independently to determine the nature of the slope of BC.

Let's combine them.
(1)We have a line AB that makes 45 degrees with the negative X-axis but we don't know if A is on the top-left or B is on the top-left.
(2)Then a line BC has to make 37 degrees with AB. In each of the two cases above, BC can be drawn in two directions.

So, there are a total of four cases(as shown in the image below).

Image

[spoiler](C)[/spoiler] is the answer
so the trick is to recognize right away that -1 slope gives a 45 degree angle against the Y axis.. great explanation Aneesh!
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