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Bunuel
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Ans: E
Stmnt 1: no clear info..line with positive slope could exist in any of the four quadrants ( line with eqn x=y positive slope but exists in 1st and 3rd quadrant only; line with eqn y=x+6 passes through 1st ,2nd & 3rd quadrant). Hence insufficient.

Stmnt 2: i think it gives info about x or y intercepts taken one at a time.Experts please clarify if i have deduced wrong.Still insufficient considering positive and negetive x and/or y intercepts.

Combining 1&2 : positive slope with intercept of 3 units can exist and yet not be in 2nd quadrant.Eg: y=x-3 ( slope =+1 and y -intercept 3 units , but passes through 1st , 3rd and 4th quadrant only.)
Hence insufficient.
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Bunuel
Line L is a line in the x-y plane. Does line L pass through the second quadrant?

(1) Line L has a positive slope
(2) At its closest approach, Line L is never closer than 3 units to the origin.

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Statement #1: Line L has a positive slope
Case one — line below origin goes through quadrants III, IV, and I.
Attachment:
gsdsq_img9.png
gsdsq_img9.png [ 31.84 KiB | Viewed 6073 times ]
Case two — line through origin goes through just quadrants III & I.
Attachment:
gsdsq_img10.png
gsdsq_img10.png [ 33.84 KiB | Viewed 6074 times ]
Case three — line below origin goes through quadrants III, II, and I.
Attachment:
gsdsq_img11.png
gsdsq_img11.png [ 25.02 KiB | Viewed 6025 times ]

Some lines with positive slopes go through Quadrant II, and some do not. Statement #1, alone and by itself, is insufficient.

Statement #2: At its closest approach, Line L is never closer than 3 units to the origin.
In the diagram below, the red circle has a radius of three, and no line crosses within this circle — thus, every line in this diagram meets the condition given in Statement #2.
Attachment:
gsdsq_img12.png
gsdsq_img12.png [ 70.65 KiB | Viewed 6009 times ]

All lines with negative slopes pass through Quadrant II. Vertical lines pass through Quadrant II only if they are to the left of the y-axis. Horizontal lines pass through Quadrant II only if they are above the x-axis. As we saw in statement #1, some lines with positive slope pass through Quadrant II and some don’t. Statement #2, alone and by itself, is insufficient.

Statements #1 & #2 combined: Now, we are confined to lines with positive slopes and we also have the red circle. The following diagram tells the whole story:
Attachment:
gsdsq_img13.png
gsdsq_img13.png [ 23.95 KiB | Viewed 5983 times ]
Both of these lines meet both conditions — positive slopes and outside the red circle. One of them passes through Quadrant II, and one of the them doesn’t. Therefore, even if we know both conditions are true, that will not answer the prompt question. Combined, the statements are still insufficient.

Answer = E.
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Just adding my 2c below,

Pushing the equation / Translation

Does the line pass through the second quadrant?
- Positive lines can do this if the X-intercept is negative, Negative lines can do this whether the X-intercept is negative or positive

Statement 1. Line L has a positive slope
- Could be a line with a negative X-intercept
- Could be a line with a positive X-intercept
- Thus, INSUFFICIENT

Statement 2. At its closest approach, Line L is never closer than 3 units to the origin
- Could be a line with a positive slope and negative X-intercept
- Could be a line with a negative slope and negative X-intercept (cutting through QIII as well)
- Could be a line with a negative slope and positive X-intercept (Cutting through QI as well)

Both - only positively sloped line scenarios with X-intercept never >-3 or <3
- Could be a line with a negative X-intercept
- Could be a line with a positive X-intercept

Therefore, Option E
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