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.
Answer = C.