Does line L pass through the Quadrant II?

Question

(1) Line L has a positive slope

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

GMATinsight · Answer

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

Answer: Option E

GyMrAT · Answer

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.

Answer E.

Thanks,
GyM

Prep Toolkit