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# Is the slope of Line 1 positive?

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Re: Is the slope of Line 1 positive? [#permalink]
(1) Insufficient. Several possibilities for Line 1 and Line 2 to make an angle of 40 degrees.
(2) Insufficient. Clearly insufficient.

(1)+(2) Insufficient . If Line 1 is in the I and III quadrants and makes 40 degree angle with Line 2, the slope of Line 1 is positive. If the Line 1 is in the II and IV quadrants and makes a 40 degree angle with Line 2, the slope of Line 2 is negative.

(I am not sure if it is possible for Line 1 with negative slope to make a 40 degree angle with a Line 2, though..)

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Re: Is the slope of Line 1 positive? [#permalink]
My approach is quite simple and mathematical.We can calculate the angle between two lines by below formula

Tan (A-B) =(Tan A -Tan B)/1-2Tan A*TanB)

so from 1 ,angle between A and B is given ----insufficient

from 2 , angle B is given i.e 45 ----insufficient

By combining 1 and 2

we know A-B and also B ,we can calculate A ,though no need to calculate ...if A<90 then slope is + else -
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Re: Is the slope of Line 1 positive? [#permalink]
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Bunuel wrote:
Bunuel wrote:
Is the slope of Line 1 positive?

(1) The angle between Line 1 and Line 2 is 40º.
(2) Line 2 has a slope of 1

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

A straightforward prompt.

Statement #1 is intriguing: it gives us a specific angle measure. This is tantalizing, but unfortunately, it is only the angle between Line 1 and Line 2, and that angle could be oriented in any direction. Therefore, we can draw no conclusion about the prompt from this statement alone. Statement #1, by itself, is insufficient.

Statement #2 is also tantalizing, because it’s numerically specific. But, unfortunately, this tells us a lot about Line 2 and zilch about Line one, so this statement is, by itself, is also insufficient.

Now, combine the statements. From statement #2, we know Line 2 has a slope of 1, which means the angle between Line 2 and the positive x-axis is 45º. We know, from statement #1, that Line #1 is 40º away from Line 2. We don’t know which way, above or below Line 2. If Line 1 is steeper than Line 2, it makes an angle of 45º + 40º = 85º with the positive x-axis. If Line 1 is less steep than Line 2, it makes an angle of 45º – 40º = 5º with the positive x-axis. Either way, its angle above the positive x-axis is between 0º and 90º, which means it has a positive slope. The combined statements allow us to give a definitive answer to the prompt question.

Quick question: When the statement mentions angle between line 1 and line 2, is it always in reference to point of origin? See highlighted. Can you diagrammatically show me how to visualize this? Why can't -see attached- be a possible case?
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Re: Is the slope of Line 1 positive? [#permalink]
TheMechanic wrote:
Bunuel wrote:
Bunuel wrote:
Is the slope of Line 1 positive?

(1) The angle between Line 1 and Line 2 is 40º.
(2) Line 2 has a slope of 1

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

A straightforward prompt.

Statement #1 is intriguing: it gives us a specific angle measure. This is tantalizing, but unfortunately, it is only the angle between Line 1 and Line 2, and that angle could be oriented in any direction. Therefore, we can draw no conclusion about the prompt from this statement alone. Statement #1, by itself, is insufficient.

Statement #2 is also tantalizing, because it’s numerically specific. But, unfortunately, this tells us a lot about Line 2 and zilch about Line one, so this statement is, by itself, is also insufficient.

Now, combine the statements. From statement #2, we know Line 2 has a slope of 1, which means the angle between Line 2 and the positive x-axis is 45º. We know, from statement #1, that Line #1 is 40º away from Line 2. We don’t know which way, above or below Line 2. If Line 1 is steeper than Line 2, it makes an angle of 45º + 40º = 85º with the positive x-axis. If Line 1 is less steep than Line 2, it makes an angle of 45º – 40º = 5º with the positive x-axis. Either way, its angle above the positive x-axis is between 0º and 90º, which means it has a positive slope. The combined statements allow us to give a definitive answer to the prompt question.

Quick question: When the statement mentions angle between line 1 and line 2, is it always in reference to point of origin? See highlighted. Can you diagrammatically show me how to visualize this? Why can't -see attached- be a possible case?

Bunuel chetan2u i have the same doubt , can anyone please throw some light on this .
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Re: Is the slope of Line 1 positive? [#permalink]
TheMechanic wrote:
Bunuel wrote:
Bunuel wrote:
Is the slope of Line 1 positive?

(1) The angle between Line 1 and Line 2 is 40º.
(2) Line 2 has a slope of 1

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

A straightforward prompt.

Statement #1 is intriguing: it gives us a specific angle measure. This is tantalizing, but unfortunately, it is only the angle between Line 1 and Line 2, and that angle could be oriented in any direction. Therefore, we can draw no conclusion about the prompt from this statement alone. Statement #1, by itself, is insufficient.

Statement #2 is also tantalizing, because it’s numerically specific. But, unfortunately, this tells us a lot about Line 2 and zilch about Line one, so this statement is, by itself, is also insufficient.

Now, combine the statements. From statement #2, we know Line 2 has a slope of 1, which means the angle between Line 2 and the positive x-axis is 45º. We know, from statement #1, that Line #1 is 40º away from Line 2. We don’t know which way, above or below Line 2. If Line 1 is steeper than Line 2, it makes an angle of 45º + 40º = 85º with the positive x-axis. If Line 1 is less steep than Line 2, it makes an angle of 45º – 40º = 5º with the positive x-axis. Either way, its angle above the positive x-axis is between 0º and 90º, which means it has a positive slope. The combined statements allow us to give a definitive answer to the prompt question.

Quick question: When the statement mentions angle between line 1 and line 2, is it always in reference to point of origin? See highlighted. Can you diagrammatically show me how to visualize this? Why can't -see attached- be a possible case?

For Line 1 to have a negative slope, it will need to make at least a 45º angle with Line 2. (assume Line 1 to be parallel to X axis, now it has a 45º angle with line 2. To make line 1 have a negative slope, one needs to increase the angle with line 2 beyond 45º. One can increase this angle up to 135º. Beyond 135º, Line 1 will have a positive slope again.)

Hope this helps!
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Re: Is the slope of Line 1 positive? [#permalink]
TheMechanic wrote:
Bunuel wrote:
Bunuel wrote:
Is the slope of Line 1 positive?

(1) The angle between Line 1 and Line 2 is 40º.
(2) Line 2 has a slope of 1

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

A straightforward prompt.

Statement #1 is intriguing: it gives us a specific angle measure. This is tantalizing, but unfortunately, it is only the angle between Line 1 and Line 2, and that angle could be oriented in any direction. Therefore, we can draw no conclusion about the prompt from this statement alone. Statement #1, by itself, is insufficient.

Statement #2 is also tantalizing, because it’s numerically specific. But, unfortunately, this tells us a lot about Line 2 and zilch about Line one, so this statement is, by itself, is also insufficient.

Now, combine the statements. From statement #2, we know Line 2 has a slope of 1, which means the angle between Line 2 and the positive x-axis is 45º. We know, from statement #1, that Line #1 is 40º away from Line 2. We don’t know which way, above or below Line 2. If Line 1 is steeper than Line 2, it makes an angle of 45º + 40º = 85º with the positive x-axis. If Line 1 is less steep than Line 2, it makes an angle of 45º – 40º = 5º with the positive x-axis. Either way, its angle above the positive x-axis is between 0º and 90º, which means it has a positive slope. The combined statements allow us to give a definitive answer to the prompt question.

Quick question: When the statement mentions angle between line 1 and line 2, is it always in reference to point of origin? See highlighted. Can you diagrammatically show me how to visualize this? Why can't -see attached- be a possible case?

Dear GMATGuruNY

Is not the above diagram a possible solution?
Thanks
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Re: Is the slope of Line 1 positive? [#permalink]
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Mo2men wrote:
Dear GMATGuruNY

Is not the above diagram a possible solution?
Thanks

Statements combined:
From Line 2, Line 1 must be rotated 40 degrees clockwise or 40 degrees counter-clockwise.
If the two lines intersect at the origin, we get:

Each option for Line 1 has a positive slope -- a condition that will hold true no matter where the two lines intersect on the coordinate plane.
Thus, the answer to the question stem is YES.
SUFFICIENT.

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Re: Is the slope of Line 1 positive? [#permalink]
1
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GMATGuruNY wrote:
Mo2men wrote:
Dear GMATGuruNY

Is not the above diagram a possible solution?
Thanks

Statements combined:
From Line 2, Line 1 must be rotated 40 degrees clockwise or 40 degrees counter-clockwise.
If the two lines intersect at the origin, we get:

Each option for Line 1 has a positive slope -- a condition that will hold true no matter where the two lines intersect on the coordinate plane.
Thus, the answer to the question stem is YES.
SUFFICIENT.

Dear GMATGuruNY

But here is my question. You says: "If the two lines intersect at the origin"....So here you assumed they both intersect in the origin but nothing in the question says so.

It is still the graph below valid. The intersection is not mandatory to be in origin here. So it rotates 40 degrees from another point in line 2.

Where did I go wrong?

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Re: Is the slope of Line 1 positive? [#permalink]
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Mo2men wrote:
But here is my question. You says: "If the two lines intersect at the origin"....So here you assumed they both intersect in the origin but nothing in the question says so.

As mentioned in my post, the result will be the same no matter where the two lines intersect.

Quote:
It is still the graph below valid. The intersection is not mandatory to be in origin here. So it rotates 40 degrees from another point in line 2.

Where did I go wrong?

In your drawing, the angle labeled as 40 degrees is actually well over 45 degrees.

In the figure above, the horizontal red line forms a 45 degree angle with Line 2.
Clearly, the angle labeled as 40 degrees is actually far greater than 45 degrees.
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Re: Is the slope of Line 1 positive? [#permalink]
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Re: Is the slope of Line 1 positive? [#permalink]
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