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Slope is positive for a line in 1st and 3rd quadrant. 1) Insufficient as the two lines can be in any quadrant. 2) The slope is one is y=x line going trough 1 and 3 but no relation to line 1 so insufficient.

40 degree angle will still make the line 1 be in quadrant 1 ans 3 as the line 2 has 45 degree angle with horizontal. sufficient answer is C.

(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..)

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.

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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.

Answer = C.

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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