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# Does line L pass through the Quadrant II?

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Math Expert
Joined: 02 Sep 2009
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13 Aug 2018, 03:29
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Difficulty:

25% (medium)

Question Stats:

76% (00:55) correct 24% (00:42) wrong based on 59 sessions

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Does line L pass through the Quadrant II?

(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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13 Aug 2018, 06:19
Bunuel wrote:
Does line L pass through the Quadrant II?

(1) Line L has a positive slope

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

Question: Does line L pass through the Quadrant II?

FACT: Any line that has Negative slope will always pass through Quadrant II and IV

Statement 1: Line L has positive slope

NOT SUFFICIENT

Statement 2: At its closest approach, Line L is never closer than 3 units to the origin.

Line may or may NOT have negative slope and hence

Not sufficient

COmbining the two statements:

Make a circle of radius 3 and draw a line of positive slope outside the circle

One line above circle will pass through quad II and line below circle won't pass through Quad II hence

NOT SUFFICIENT

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13 Aug 2018, 12:24
Bunuel wrote:
Does line L pass through the Quadrant II?

(1) Line L has a positive slope

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

Statement 1: Line L has a positive slope

Hence Line L can pass through Quadrant 2 with a positive y-intercept & it can also pass through Quadrant 4 with a negative y-intercept.

Statement 1 alone is not sufficient.

Statement 2: At its closest approach, Line L is never closer than 3 units to the origin

Clearly not sufficient, as the line can lie in any quadrant at a distance of 3 units from the origin.

Combining, we can still have the line in Quadrant 2 or in Quadrant 4 at a distance of 3 units from the origin.

Hence combining is Not Sufficient.

Thanks,
GyM
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Re: Does line L pass through the Quadrant II?   [#permalink] 13 Aug 2018, 12:24
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